Tank Volume Calculator
Calculate tank capacity, current liquid volume, percent full, remaining capacity, or the liquid depth required for a target volume using inside tank dimensions.
Calculator is for informational purposes only. Terms and Conditions
The active equation changes with tank shape and calculation mode. Partial horizontal-cylinder volume uses circular-segment geometry, so liquid depth is not proportional to volume.
Choose the tank and calculation
Select the tank geometry, what you want to calculate, and your preferred unit system.
Enter tank dimensions
Use inside dimensions for geometric liquid capacity. Fields change automatically for the selected tank shape.
Fields marked required must be completed. You may mix supported units; each unit change converts the existing physical quantity.
Result
The primary answer appears first, followed by capacity, fill percentage, remaining capacity, warnings, and transparent calculation steps.
Result details
- Check—
Show calculation steps Review conversions, geometry, substitutions, assumptions, and checks
- Enter valid values to see the complete calculation.
Tank Fill Diagram
A simplified geometric view of the selected tank. The liquid shading follows the calculated fill depth; numerical results remain in the result card above.
Method, Sources, and Assumptions
Calculation basis, unit references, geometry scope, limitations, and verification requirements.
Volumes are calculated from standard solid-geometry relationships. U.S. gallon, Imperial gallon, and liter conversions follow NIST conversion factors. Partial horizontal-cylinder volume uses the area of a circular segment multiplied by tank length.
- Use inside dimensions. Outside dimensions require a separate wall-thickness correction before using this geometric model.
- Calculated capacity is ideal geometric volume and does not account for fittings, baffles, coils, deformation, tilt, dead volume, or manufacturing tolerances.
- The horizontal-cylinder model uses flat ends; dished, hemispherical, ellipsoidal, and torispherical heads are outside this version’s scope.
- For calibrated, custody-transfer, regulated, or safety-critical tanks, verify capacity using the applicable tank calibration method, drawings, manufacturer data, and project requirements.
Calculator guide
How to Calculate Tank Volume
The Tank Volume Calculator above determines full tank capacity, liquid volume at a measured level, percent full, remaining capacity, or the liquid depth required for a target volume. Choose the tank shape, enter the required inside dimensions, and select the calculation you need. The tool supports horizontal and vertical cylinders, rectangular tanks, spheres, and vertical conical frustums, with U.S. customary and metric units.
For full tanks, volume comes directly from the tank’s ideal internal geometry. For a partially filled tank, the liquid volume depends on how the cross-sectional area changes with depth. That distinction matters most for horizontal cylinders, spheres, and tapered tanks, where a given percentage of liquid depth does not generally equal the same percentage of tank volume.
- Best for
- Geometric capacity and partial-fill checks for common tank shapes
- Main outputs
- Capacity, liquid volume, percent full, remaining capacity, or required depth
- Key assumption
- Dimensions represent the ideal inside tank geometry
How to Use the Tank Volume Calculator
Start with the tank geometry and the quantity you know. The calculator changes the required fields automatically, converts existing values when you change units, and keeps the primary result ahead of the supporting checks.
-
Choose the tank shape
Select Horizontal cylinder, Vertical cylinder, Rectangular tank, Spherical tank, or Vertical conical frustum. Use the shape that represents the tank’s internal liquid space, not merely its exterior appearance.
-
Choose what to calculate
Select Full tank capacity, Liquid volume from depth, or Required depth for target volume. Partial-fill mode uses a measured level; reverse mode starts with a target liquid volume and solves for the corresponding depth.
-
Enter inside dimensions and the level measurement
Enter only the dimensions shown for the selected shape. In Liquid volume from depth mode, Advanced Options lets you define the entered level as liquid depth from the bottom or ullage from the top. Ullage is the empty vertical distance from the inside top of the tank down to the liquid surface.
-
Review the result and cross-checks
For partial-fill calculations, compare liquid volume, full capacity, percent full, and remaining capacity. You can also switch answer units among supported gallon, liter, and cubic-volume units, or length units when solving for required depth.
Tank Volume Formulas and Calculation Method
The calculator uses exact ideal-geometry relationships for the supported shapes. Full capacity is a closed-form geometry calculation. Partial-fill volume is also closed form for the supported shapes, while the reverse target-volume mode uses a bounded numerical solve when depth cannot be isolated conveniently.
| Tank shape | Full-volume relationship | Dimensions |
|---|---|---|
| Horizontal cylinder | \(V=\pi r^2L\) | Inside radius \(r\), straight inside length \(L\) |
| Vertical cylinder | \(V=\pi r^2H\) | Inside radius \(r\), inside height \(H\) |
| Rectangular tank | \(V=LWH\) | Inside length \(L\), width \(W\), height \(H\) |
| Sphere | \(V=\frac{4}{3}\pi r^3\) | Inside radius \(r\) |
| Vertical conical frustum | \(V=\frac{\pi H}{3}(r_1^2+r_1r_2+r_2^2)\) | Bottom radius \(r_1\), top radius \(r_2\), height \(H\) |
Partially filled horizontal cylinder
Plain language: find the filled circular-segment area at liquid depth \(h\), then multiply that area by the straight tank length \(L\).
The valid liquid-depth range is from empty, \(h=0\), to full, \(h=2r\). At \(h=r\), the tank is exactly half full. At other depths the relationship is nonlinear.
Partially filled spherical tank
For a spherical tank, liquid measured upward from the bottom forms a spherical cap of height \(h\). The formula reaches half the sphere volume when the liquid surface passes through the sphere center.
Partially filled vertical conical frustum
The local radius \(r_h\) changes linearly from the bottom radius \(r_1\) to the top radius \(r_2\). The calculator uses that radius to evaluate the smaller frustum occupied by liquid up to depth \(h\).
Why horizontal tank depth is not the same as percent full
A horizontal cylinder is narrow near the bottom and top and widest at mid-height. As a result, each additional inch of depth adds a different amount of volume. The table below is dimensionless, so the percentages apply to any ideal horizontal cylinder regardless of diameter or length.
| Liquid depth | Tank volume |
|---|---|
| 10% of diameter | About 5.20% full |
| 25% of diameter | About 19.55% full |
| 50% of diameter | 50.00% full |
| 75% of diameter | About 80.45% full |
| 90% of diameter | About 94.80% full |
Reverse target-volume calculation
When you select Required depth for target volume, the calculator solves \(V(h)=V_{\text{target} }\) within the physical interval from empty to full depth. For shapes where a simple algebraic rearrangement is not practical, a bounded bisection solve repeatedly narrows the valid depth range until the calculated volume matches the target within the numerical tolerance.
Horizontal Tank Partial-Fill Example
Consider a flat-ended horizontal cylindrical tank with a 48-inch inside diameter, a 72-inch straight inside length, and 12 inches of liquid depth. The depth is 25% of the diameter, but the tank is not 25% full.
Substitute the dimensions
This gives approximately \(25{,}471.47\text{ in}^3\) of liquid.
Convert cubic inches to U.S. gallons
The full tank holds approximately \(564.02\) U.S. gallons, so the liquid occupies about \(19.55\%\) of full geometric capacity.
Result
Liquid volume ≈ 110.27 US gal; tank fill ≈ 19.55%
A quarter of the diameter in liquid depth corresponds to less than a quarter of the volume because the tank cross-section is narrower near the bottom.
How to Interpret Tank Volume Results
Treat the calculator’s main result as ideal geometric volume or depth for the dimensions you entered. For partial fills, the supporting values make it easy to check whether the result is physically consistent before you use it for planning.
Capacity, liquid volume, and remaining capacity
Full capacity is the ideal volume at 100% fill. Current liquid volume is the portion occupied at the calculated depth. Remaining capacity is the difference: \(V_{\text{remaining} }=V_{\text{full} }-V_{\text{liquid} }\).
Diameter errors grow quickly
For a cylindrical tank with length held constant, full volume varies with diameter squared. Increasing diameter by 10% increases calculated full volume by \(1.1^2-1=21\%\). A diameter measurement error therefore matters more than the same percentage error in length.
Fast physical checks
Liquid volume must stay between zero and full capacity, remaining capacity cannot be negative, and liquid depth or ullage cannot exceed the tank’s internal vertical depth. In reverse mode, target volume must not exceed full capacity.
Measurements, Units, and Common Input Errors
Most large tank-volume errors come from measuring the wrong geometry rather than from the volume formula itself. Use actual inside dimensions, confirm whether a measurement is diameter or radius, and distinguish liquid depth from ullage before relying on the result.
- Use inside dimensions. Outside diameter or outside length includes wall thickness and can overstate internal liquid capacity. For a uniform cylindrical wall, \(D_i=D_o-2t\), where \(t\) is wall thickness.
- Do not enter radius as diameter. The calculator’s cylinder and sphere inputs use inside diameter. Radius is one-half of diameter: \(r=D/2\).
- For horizontal cylinders, use straight cylindrical length. The supported horizontal-cylinder geometry has flat ends. Overall end-to-end length of a tank with dished or rounded heads does not represent the straight cylindrical length used by this model.
- Distinguish liquid depth from ullage. Liquid depth is measured upward from the internal bottom. Ullage is measured downward from the internal top. When ullage is used, the calculator converts it to liquid depth before evaluating volume.
- Mixed units are allowed, but each dimension still represents a physical measurement. Changing an individual unit or the U.S./SI preset converts the existing value instead of simply changing the label.
| Volume unit | Equivalent |
|---|---|
| 1 U.S. gallon | 3.785411784 L |
| 1 Imperial gallon | 4.54609 L |
| 1 cubic foot | 28.316846592 L |
| 1 cubic meter | 1,000 L |
The calculator’s U.S. gallon, Imperial gallon, cubic-foot, cubic-inch, liter, and cubic-meter conversions are consistent with NIST Guide to the SI volume conversion factors.
Assumptions and Limits of Geometric Tank Volume
This calculator models ideal internal geometry. That is appropriate for dimensional capacity checks, but a real tank’s calibrated or usable operating volume can differ from the geometric result.
Ideal shape
The model does not subtract volume occupied by baffles, coils, dip tubes, internal piping, fittings, sediment, or other obstructions. It also does not model dents, deformation, tilt, or manufacturing tolerances.
Flat-ended horizontal cylinders
The horizontal-cylinder calculation treats the tank as a straight cylinder with flat ends. Hemispherical, ellipsoidal, torispherical, or other dished heads require additional head geometry.
Linear frustum taper
The vertical conical-frustum model assumes a circular radius that changes linearly from the bottom diameter to the top diameter over the entered vertical height.
Geometric capacity is not an operating limit
A calculated 100% geometric capacity does not establish a permissible maximum fill level, required freeboard, thermal-expansion allowance, overflow margin, or code-compliant operating volume.
Sources and Calculation Verification
The calculator combines standard solid geometry, circular-segment geometry for a horizontal cylinder, spherical-cap geometry for a partially filled sphere, a linearly tapered conical-frustum model, and NIST-consistent volume conversions. The worked example above was independently recomputed from the dimensionless fill fraction as a cross-check.
- NIST Guide to the SI, Appendix B.9 — Volume conversion factors — supports U.S. gallon, Imperial gallon, cubic-foot, cubic-inch, liter, and cubic-meter conversions.
- Wolfram MathWorld — Circular Segment — gives the circular-segment area relationship used for liquid depth in an ideal horizontal cylindrical tank.
- Wolfram MathWorld — Spherical Cap — supports the spherical-cap volume relationship used for partial spherical-tank volume.
- Wolfram MathWorld — Conical Frustum — supports the frustum volume relationship and linearly varying radius model.
- American Petroleum Institute — Petroleum Measurement Standards Committees — identifies MPMS chapters covering tank calibration, tank gauging, and calculation of petroleum quantities.
The article and calculator use geometric capacity as a mathematical estimate from entered dimensions. They do not claim certified tank calibration, code compliance, manufacturer approval, or a universal allowable operating fill level.