Orifice Flow Calculator
Calculate flow rate, required orifice bore, or differential pressure for a concentric sharp-edged orifice plate in a full pipe.
Calculator is for informational and preliminary engineering purposes only. Terms and Conditions
The discharge coefficient is solved iteratively with the Reader-Harris/Gallagher correlation; gas/vapor mode also applies the ISO expansibility factor using upstream absolute pressure.
Choose the calculation setup
Select the unknown, fluid phase, and standardized pressure-tap arrangement.
Enter the known values
Use actual internal diameters and fluid properties at the upstream operating condition.
Values update automatically. Changing a unit converts the represented physical quantity rather than reinterpreting the number.
Result
Primary answer first, followed by flow checks, ISO applicability status, and transparent calculation steps.
Engineering checks
- Check—
Show calculation stepsReview conversions, coefficient iteration, substitutions, assumptions, and checks
- Enter valid values to see the complete calculation.
Orifice plate geometry
The bore opening updates with beta ratio; pressure-tap markers update with the selected tap arrangement.
Method, Sources, and Assumptions
Calculation basis, current standard scope, example-property basis, limitations, and final verification requirements.
The calculator uses the ISO 5167 differential-pressure relationship with the Reader-Harris/Gallagher discharge-coefficient correlation for flange, corner, or D and D/2 taps. Liquid mode uses ε = 1; gas/vapor mode uses the ISO orifice expansibility relationship. Permanent pressure loss is estimated with the ISO 5167-2 pressure-loss relation using the solved beta ratio and discharge coefficient.
- The loaded 100 mm pipe, 50 mm bore, 10 kPa differential pressure, 998.2 kg/m³ density, and 1.002 mPa·s viscosity form an illustrative water-like example; they are not design recommendations.
- This tool does not verify plate edge geometry, plate thickness, pipe roughness, straight-run lengths, tapping construction, pulsation, swirl, multiphase flow, subsonic condition, or installation details required by the standard.
- Use measured or authoritative fluid properties at the actual upstream operating state. Switching between liquid and gas/vapor mode does not automatically change density or viscosity.
- Final metering or design decisions require the complete applicable standard, instrument/manufacturer requirements, field conditions, and qualified engineering judgment.
Calculator guide
Understanding Your Orifice Flow Calculator Result
The Orifice Flow Calculator above determines volumetric flow rate, required orifice bore diameter, or differential pressure for a concentric orifice plate installed in a full pipe. Depending on the selected solve mode, it uses pipe inside diameter, orifice bore, differential pressure or target flow, upstream fluid density, dynamic viscosity, pressure-tap arrangement, and compressibility inputs for gases or vapors.
The calculation is based on the differential-pressure orifice-meter relationship rather than the simpler equation used for a free jet leaving a tank. The calculator also evaluates the discharge coefficient from the operating Reynolds number, applies a gas expansibility correction when required, and reports beta ratio, Reynolds number, mass flow, velocity, estimated permanent pressure loss, and an ISO 5167 calculation-range check.
- Best for
- Concentric differential-pressure orifice plates in full circular pipes
- Solve for
- Flow rate, orifice bore diameter, or differential pressure
- Key check
- Use actual pipe ID and fluid properties at the upstream operating condition
How to Use the Orifice Flow Calculator
Start by choosing the quantity you need to determine. The calculator changes the required fields automatically, so only the known values needed for the selected solve mode are used.
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Choose what to solve for
Select Flow rate when the pipe, bore, differential pressure, and fluid properties are known. Select Orifice bore diameter when you know the target flow and available differential pressure. Select Differential pressure when you know the required flow through an existing pipe and bore.
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Select liquid or gas/vapor service
Use Liquid / incompressible when the incompressible treatment is appropriate. Gas or vapor mode adds upstream absolute pressure and isentropic exponent because the fluid expands as pressure decreases through the restriction. Changing the phase selector does not automatically change density or viscosity, so those values still need to represent the actual fluid state.
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Select the pressure-tap arrangement
The calculator provides flange taps, corner taps, and D and D/2 taps. Tap location matters because the Reader–Harris/Gallagher discharge-coefficient correlation includes the standardized pressure-tap geometry.
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Enter the actual pipe and orifice geometry
Use the pipe’s actual inside diameter, not its nominal pipe designation. When flow rate or differential pressure is being solved, enter the actual concentric orifice bore diameter. The beta ratio is then calculated from \( \beta=d/D \).
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Enter differential pressure or target flow
Differential pressure is the upstream static pressure minus the downstream static pressure measured at the selected tap locations. The calculator accepts Pa, kPa, MPa, bar, mbar, psi, inH₂O, and mmH₂O. Target flow can be entered in m³/s, m³/h, L/s, L/min, US gpm, or ft³/min when using a reverse solve mode.
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Use fluid properties at the upstream state
Enter upstream density and dynamic viscosity for the actual fluid, pressure, and temperature. Density directly affects the pressure-to-flow relationship, while viscosity affects Reynolds number and therefore the calculated discharge coefficient.
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Review more than the primary answer
After the main result, check beta ratio, discharge coefficient, Reynolds number, expansibility factor, pipe and orifice-area velocities, estimated permanent pressure loss, and the ISO 5167 calculation-range status. A numerical result can still require caution when a range check is outside the calculator’s validated domain.
Orifice Flow Calculator Inputs and Outputs
The calculator supports mixed engineering units while preserving the same underlying physical quantity when a unit selector changes. The table below summarizes the main fields and the quantities they represent.
| Quantity | Symbol | Role | Supported units |
|---|---|---|---|
| Pipe internal diameter | \(D\) | Geometry input | mm, cm, m, in, ft |
| Orifice bore diameter | \(d\) | Geometry input or sizing result | mm, cm, m, in, ft |
| Differential pressure | \(\Delta p\) | Input or reverse-solved result | Pa, kPa, MPa, bar, mbar, psi, inH₂O, mmH₂O |
| Target volumetric flow | \(Q\) | Input for bore or DP solve | m³/s, m³/h, L/s, L/min, US gpm, ft³/min |
| Upstream density | \(\rho_1\) | Fluid-property input | kg/m³, lb/ft³ |
| Dynamic viscosity | \(\mu\) | Reynolds-number input | Pa·s, mPa·s, cP, lb/(ft·s) |
| Upstream absolute pressure | \(p_1\) | Gas/vapor input | Pa abs, kPa abs, bar abs, psia |
| Isentropic exponent | \(\kappa\) | Gas/vapor input | Dimensionless |
| Volumetric flow result | \(Q\) | Primary result in flow mode | m³/s, m³/h, L/s, L/min, US gpm, ft³/min |
Orifice Flow Calculation Method
For a concentric orifice plate in a full pipe, the measured differential pressure is related to flow through the orifice area, the pipe-to-bore diameter ratio, the discharge coefficient, fluid density, and—when the fluid is compressible—the expansibility factor.
Volumetric flow equation
In plain language, flow increases with orifice area and approximately with the square root of differential pressure. The discharge coefficient corrects the idealized flow model, the beta term accounts for upstream approach velocity in the full pipe, and the expansibility factor corrects gas or vapor expansion.
The calculator evaluates \(C\) rather than assuming a single constant value. In flow-rate mode it iterates flow, Reynolds number, and the Reader–Harris/Gallagher discharge coefficient until the solution converges.
Gas or vapor expansibility
For the calculator’s incompressible-liquid mode, \( \varepsilon=1 \). Gas or vapor mode calculates a value that reflects density change through the pressure reduction and therefore requires upstream absolute pressure and the fluid’s isentropic exponent.
Why the discharge coefficient is not simply 0.61
A value near 0.61 is often useful for rough sharp-edged-orifice estimates, but a differential-pressure metering plate is more specific. In this calculator, the discharge coefficient depends on beta ratio, pipe Reynolds number, pipe diameter, and the selected pressure-tap locations. Because Reynolds number itself depends on flow, the flow-rate solution is iterative.
Why the beta-ratio correction appears
The simple free-orifice relationship assumes an upstream reservoir or another condition where approach velocity can be neglected. In a full pipe, fluid already has measurable velocity before reaching the plate. The \(1/\sqrt{1-\beta^4}\) term accounts for that velocity-of-approach effect. This is one reason a tank-opening calculation and an ISO-style pipe-orifice calculation should not be treated as interchangeable.
Reynolds number in the orifice calculation
Reynolds number connects the calculated flow to viscous effects in the upstream pipe. It is used by the discharge-coefficient correlation and is also part of the calculator’s calculation-range checks.
- \(Q\)
- Volumetric flow rate Fluid volume passing through the pipe per unit time at the upstream density used in the calculation.
- \(C\)
- Discharge coefficient Empirical correction evaluated from the Reader–Harris/Gallagher relationship for the operating point and tap arrangement.
- \(\varepsilon\)
- Expansibility factor Compressibility correction for gas or vapor flow; equal to 1 in the calculator’s incompressible-liquid mode.
- \(A_o\)
- Orifice area Cross-sectional area of the circular orifice bore, \(A_o=\pi d^2/4\).
- \(\beta\)
- Beta ratio Ratio of orifice bore diameter to pipe internal diameter, \(d/D\).
- \(d\)
- Orifice bore diameter Diameter of the concentric opening through the orifice plate.
- \(D\)
- Pipe internal diameter Actual inside diameter of the upstream pipe at the measuring section.
- \(\Delta p\)
- Differential pressure Static-pressure difference between the selected upstream and downstream pressure taps.
- \(\rho_1\)
- Upstream fluid density Density at the upstream operating pressure and temperature.
- \(\mu\)
- Dynamic viscosity Fluid resistance to shear used when calculating the upstream pipe Reynolds number.
- \(Re_D\)
- Pipe Reynolds number Dimensionless measure of inertial relative to viscous effects using the upstream pipe diameter.
- \(p_1\)
- Upstream absolute pressure Absolute static pressure upstream of the plate, required by the gas/vapor expansibility calculation.
- \(p_2\)
- Downstream pressure Pressure corresponding to \(p_1-\Delta p\) for the gas expansibility calculation.
- \(\kappa\)
- Isentropic exponent Fluid-specific heat-capacity ratio used by the calculator’s gas/vapor expansibility relationship.
Worked Orifice Flow Example
Consider the calculator’s illustrative liquid example: a 100 mm inside-diameter pipe with a 50 mm concentric bore and 10 kPa differential pressure. The entered fluid properties are 998.2 kg/m³ density and 1.002 mPa·s dynamic viscosity, with flange pressure taps.
Convert the units
The diameter ratio is \( \beta=0.0500/0.100=0.500 \), and the orifice area is approximately \(0.0019635\text{ m}^2\).
Evaluate the operating-point coefficient
The discharge coefficient and Reynolds number depend on one another through the calculated flow. Iterating the Reader–Harris/Gallagher relationship for the entered flange-tap geometry gives approximately:
Substitute the values
Result
\(Q\approx19.84\text{ m}^3/\text{h}\)
The same operating point corresponds to about 5.501 kg/s mass flow, 0.702 m/s average velocity in the 100 mm pipe, and 2.807 m/s when the same volumetric flow is referenced to the orifice area.
How to Interpret the Results
The primary answer is only one part of a useful orifice calculation. The secondary results help determine whether the answer is physically reasonable, whether the empirical method is being used in an appropriate range, and what the restriction means for the piping system.
Flow and mass flow
Volumetric flow is the fluid volume per unit time at the density entered for the upstream condition. The calculator also reports mass flow as \( \dot m=\rho_1Q \). If density is wrong, the reported mass flow and the pressure-to-flow relationship will both be affected.
Square-root pressure sensitivity
Holding geometry, density, discharge coefficient, and expansibility fixed, \(Q\) is proportional to \(\sqrt{\Delta p}\). A 10% increase in differential pressure therefore produces about a 4.9% increase in flow under that controlled comparison, not a 10% increase. The exact calculator response can differ slightly because \(C\) and gas expansibility may also change.
Fast sanity check
The bore must remain smaller than the pipe ID, density and viscosity must be positive, and the differential pressure must be positive for the implemented flow direction. For gas calculations, downstream absolute pressure must also remain positive and within the pressure-ratio range used by the model.
| Relative differential pressure | Relative flow |
|---|---|
| 25% | 50.0% |
| 50% | 70.7% |
| 100% | 100% |
| 200% | 141.4% |
| 400% | 200% |
These relative values hold \(C\), \(\varepsilon\), density, and geometry constant. The live calculator can depart slightly from the ideal square-root ratios because the discharge coefficient and gas expansibility are recalculated at the new operating point.
Beta ratio
The beta ratio is simply \(d/D\), but it strongly changes the meter behavior. A smaller bore relative to the pipe generally produces more restriction and a larger differential pressure for the same flow. A larger bore reduces the restriction but also reduces the differential-pressure signal available to the measurement system. The calculator therefore reports beta explicitly rather than hiding it inside the equation.
Discharge coefficient
The discharge coefficient is an empirical correction to the idealized pressure-flow relationship. It is not an efficiency rating and it is not a universal constant for every orifice. An unusual value should prompt a check of beta ratio, Reynolds number, pipe diameter, tap selection, and the entered fluid properties.
Reynolds number
Reynolds number helps show whether the operating point falls inside the range where the implemented discharge-coefficient correlation is intended to be used. If the calculator reports an ISO 5167 calculation-range warning associated with Reynolds number, do not treat the displayed flow as a standards-qualified metering result merely because a number is available.
Differential pressure versus permanent pressure loss
The measured differential pressure \(P_1-P_2\) is the signal used to infer flow between the selected taps. Permanent pressure loss is the portion of the pressure reduction that is not recovered farther downstream. Those quantities are related but are not identical. The calculator reports a separate permanent-loss estimate using its ISO pressure-loss relationship.
Real-World Factors That Affect Orifice Flow
The equation assumes that the entered geometry, fluid properties, pressure measurements, and flow condition actually represent the installed system. A mathematically correct solution can still disagree with field performance when those conditions are not met.
Actual pipe inside diameter
Nominal pipe size is not the diameter used in the beta ratio or flow area. Schedule, lining, deposits, manufacturing tolerance, and temperature can make actual ID different from the nominal designation. Use the applicable internal diameter at the measuring section.
Fluid density and viscosity
Use properties at the upstream operating condition rather than a room-temperature value copied from an unrelated reference. Density directly enters the pressure-flow equation, while viscosity changes Reynolds number and the calculated discharge coefficient. For gases in particular, pressure and temperature can materially change density.
Plate geometry and edge condition
The calculator assumes a concentric sharp-edged metering plate represented by the implemented ISO method. It cannot inspect plate thickness, edge sharpness, bore damage, deposits, eccentric installation, or dimensional tolerances. Physical changes to the plate can change the actual discharge behavior.
Pressure-tap construction
Choosing flange, corner, or D and D/2 taps changes the discharge-coefficient calculation. The software can use the selected arrangement, but it cannot verify that the installed tap holes, locations, impulse lines, manifolds, or transmitter connections match that selection.
Upstream disturbances and flow profile
Elbows, valves, reducers, expanders, tees, swirl, and other disturbances can change the velocity profile approaching the plate. Straight-run and flow-conditioning requirements depend on the actual installation.
Pulsation and multiphase flow
The ISO 5167 scope is for single-phase, non-pulsating flow that remains subsonic through the measuring section. Wet gas, flashing, condensation, entrained liquid or gas, strong pulsation, or other multiphase behavior can invalidate the assumptions behind the displayed result.
Differential-pressure measurement
The calculated flow is only as reliable as the differential-pressure input. Check transmitter range, zero, calibration, impulse-line condition, pressure reference, and tap location when a field measurement does not agree with the expected result.
Gas absolute pressure
Gas/vapor mode requires absolute upstream pressure because the expansibility correction uses the downstream-to-upstream absolute-pressure ratio. Entering gauge pressure as though it were absolute changes that ratio and can materially distort the correction.
How much straight pipe is required?
There is no single upstream or downstream straight-run distance that is correct for every orifice meter. Required lengths depend on beta ratio and the type and arrangement of upstream disturbances such as bends, tees, valves, reducers, and expanders, as well as whether a flow conditioner is used. For a real installation, use the applicable installation requirements and tables in the current governing standard for the actual piping configuration instead of assuming one universal number of pipe diameters.
Orifice Plate Sizing and Design Checks
The calculator can reverse-solve for a required orifice bore or required differential pressure, but a mathematical solution is not automatically a finished orifice-plate specification. The solved value is an engineering input that still needs installation, instrumentation, and standards checks.
Calculated bore requirement
In Orifice bore diameter mode, the solver searches for a bore that produces the entered target flow at the entered differential pressure and fluid properties. The implemented search is constrained to beta ratios from 0.10 to 0.75 and a bore of at least 12.5 mm; if the target cannot be reached inside that search range, the calculator reports that the solution is not bracketed rather than inventing an extrapolated bore.
Selected plate and measurement system
The final plate selection must also work with the actual pipe ID, operating-flow range, allowable system pressure loss, pressure-tap arrangement, DP transmitter range and accuracy, plate construction, piping layout, and governing project requirements. Do not round the calculated bore to a convenient size without recomputing the resulting flow and differential pressure.
Balancing differential pressure and permanent loss
A smaller bore generally creates a stronger differential-pressure signal at a given flow, but it also creates greater restriction and usually greater permanent pressure loss. A larger bore reduces restriction but may produce a weaker DP signal. The appropriate tradeoff depends on the measurement range and system requirements, so there is no single beta ratio that is automatically best for every application.
Checking a DP transmitter range
Use the Differential pressure solve mode to estimate the DP generated at a known target flow and bore. Compare that result with the measurement system’s actual calibrated range, expected turndown, process pressure, and manufacturer requirements. The web calculator does not select or approve a transmitter.
Using the bore result
After solving a bore, rerun the calculation across the expected operating-flow range rather than checking only one design point. Changes in Reynolds number, fluid properties, and gas pressure ratio can shift the discharge coefficient or expansibility factor and therefore change the meter response.
Common Orifice Flow Calculation Mistakes
Most serious errors come from entering the wrong physical condition or using the wrong model, not from the arithmetic itself. Check these issues before relying on an unexpected result.
Using nominal pipe size as D
The equation requires actual internal diameter. A nominal 4-inch pipe is not automatically a 4.000-inch ID, and the resulting error affects both beta ratio and upstream pipe area.
Using the plate outside diameter
The \(d\) input is the diameter of the concentric bore through the plate, not the outside diameter of the plate or flange.
Entering gauge pressure in a gas absolute-pressure field
Gas/vapor expansibility uses a ratio of absolute pressures. Gauge pressure does not have the correct zero reference for that ratio. Convert gauge pressure to absolute pressure using the applicable local atmospheric reference before entering it as \(p_1\).
Changing the phase selector without changing properties
The calculator intentionally does not invent fluid properties. Switching from liquid to gas/vapor does not automatically replace density or viscosity. Update those inputs to values appropriate for the real upstream state.
Assuming C = 0.61 for every case
A fixed value can be useful for rough educational estimates, but this calculator’s ISO-style method evaluates the Reader–Harris/Gallagher coefficient from the current beta ratio, Reynolds number, pipe diameter, and tap configuration.
Confusing measured DP with permanent pressure loss
The pressure difference measured at the taps is not equal to the unrecovered system pressure loss. Pressure partially recovers downstream of the restriction, so review the calculator’s separate permanent-loss estimate.
Using the pipe-meter equation for a tank outlet
A tank opening discharging under a liquid head normally uses a head-based free-orifice model. The full-pipe beta correction, standardized tap geometry, and Reader–Harris/Gallagher calculation in this tool serve a different measurement problem.
Ignoring a calculation-range warning
The calculator may continue to show a numerical value for inspection when one or more ISO-style range checks fail. That does not convert the outside-range result into a standards-qualified result.
Metering Orifice Plate vs. Restriction Orifice
A metering orifice plate and a restriction orifice can look similar, but they are selected for different engineering objectives. The calculator on this page is intended for differential-pressure flow measurement, not restriction-orifice design.
| Feature | Metering orifice plate | Restriction orifice |
|---|---|---|
| Primary purpose | Determine flow from measured differential pressure | Intentionally limit flow or dissipate pressure |
| Pressure taps | Tap arrangement is part of the metering correlation | DP measurement may not be the primary design objective |
| Performance objective | Predictable pressure-to-flow relationship | Required pressure reduction or flow restriction |
| Use this calculator? | Yes, for the implemented concentric DP-metering method | No, not as a complete restriction-orifice design procedure |
Assumptions and ISO 5167 Limits
The calculator uses ISO 5167-2:2022 relationships and applicability checks for a concentric orifice plate, but software cannot verify all of the physical and installation requirements that determine whether a real meter conforms to the standard.
| Condition | Scope | Why it matters |
|---|---|---|
| Conduit | Circular conduit running full | The standard is not a general open-channel or partially full-pipe method. |
| Pressure taps | Flange, corner, or D and D/2 | These are the three tap arrangements provided by the calculator. |
| Fluid phase | Single phase | Multiphase flow can invalidate the pressure-flow relationship. |
| Flow speed | Subsonic through the measuring section | The standard does not cover a measuring section that reaches sonic conditions. |
| Pulsation | Pulsating-flow measurement is outside scope | A strongly time-varying DP signal is not represented by the steady calculation. |
| Pipe inside diameter | 50 mm to 1,000 mm | The calculator checks this overall pipe-size scope. |
| Pipe Reynolds number | Not below 5,000 | Additional Reynolds-number restrictions can apply within the detailed orifice-plate method. |
The calculator also applies its own method-specific checks for bore, beta ratio, Reynolds number, and gas pressure ratio. These checks are useful screening tools, but they do not replace the full standard or prove conformity of the installed primary element.
Concentric sharp-edged plate assumption
The implemented discharge-coefficient model is for the concentric metering geometry represented by the calculator. Do not transfer the result to a different primary element such as a Venturi tube, flow nozzle, eccentric orifice, segmental orifice, or restriction orifice without using the method appropriate to that device.
Gas pressure-ratio applicability
The calculator treats \(p_2/p_1<0.75\) as outside its ISO expansibility applicability check. In Differential pressure solve mode, the numerical search is constrained so the solved pressure ratio remains at or above 0.75 rather than presenting a normal converged result beyond that modeled range.
Properties are user supplied
The calculator does not contain an automatic fluid-property engine. Density, viscosity, upstream absolute pressure, and isentropic exponent must correspond to the real operating state. This is particularly important for gases and vapors.
Installation is not verified
The calculator cannot verify upstream straight-run requirements, flow conditioners, pipe roughness, plate edge condition, plate thickness, tap construction, swirl, pulsation, calibration, or instrument installation.
Sources and Verification Method
The calculator method and guide were checked against the current published ISO 5167 scope and authoritative fluid-property resources. The worked example was also recomputed independently and reverse-checked by solving the pressure equation from the calculated flow.
- ISO 5167-2:2022 — Orifice plates — Current published orifice-plate standard covering geometry, use, installation and operating conditions for flange, corner, and D and D/2 pressure tappings in full circular conduits.
- ISO 5167-1:2022 — General principles and requirements — General principles for differential-pressure flow devices, including measurement, installation, computation, and uncertainty requirements.
- NIST Chemistry WebBook — Thermophysical Properties of Fluid Systems — Authoritative source for properties including fluid density and viscosity at defined thermodynamic conditions.
For the calculator’s default liquid example, independent recomputation gives \(Q\approx0.0055108\text{ m}^3/\text{s}=19.84\text{ m}^3/\text{h}\). Rearranging the equation with the converged operating-point discharge coefficient reproduces the original 10 kPa differential pressure to rounding, providing a separate reverse check of the worked result.
Frequently Asked Questions
These questions cover common edge cases and next-step decisions that are not fully answered by the primary result alone.
Can the calculator be used for steam?
The interface supports a gas or vapor calculation when the required upstream density, dynamic viscosity, absolute pressure, and isentropic exponent are known. However, the ISO 5167 scope assumes single-phase flow. Wet steam, condensation, flashing, or another two-phase condition is outside that assumption and requires a more appropriate thermodynamic and flow analysis.
Can I use this calculator for natural gas?
Yes, if the entered density, viscosity, upstream absolute pressure, and isentropic exponent represent the actual upstream gas state and the pressure ratio remains within the calculator’s modeled range. The displayed volumetric result is based on the entered upstream density and is not automatically converted to SCFM or Nm³/h.
Can I use this calculator for a hole draining a tank?
No. This calculator is designed for a concentric orifice plate installed in a full pipe with differential-pressure taps. A tank outlet or free jet under liquid head normally uses a different head-based orifice-discharge model because the upstream approach condition and pressure relationship are different.
How much straight pipe is required before an orifice plate?
There is no single correct straight-run distance for every installation. Required upstream and downstream lengths depend on beta ratio, the type and arrangement of fittings or disturbances, and whether a flow conditioner is used. Check the current applicable installation requirements for the actual piping configuration.
What happens if the beta ratio is outside the calculator’s range?
The calculator can flag geometry that is outside its implemented ISO-style calculation range, and the reverse bore solver does not extrapolate beyond its configured search limits. Treat an outside-range result as a warning to review the geometry and use an appropriate validated method rather than assuming the same correlation remains accurate.