Slope Gradient Calculator

Convert between rise, run, percent grade, angle, and slope ratio. Solve for the slope gradient, the vertical rise, or the horizontal run and see angle and length along the slope as quick stats.

Configuration

Choose which quantity you want to solve for. The other fields become your known inputs.

Slope Inputs

Enter any combination of rise, run, and slope gradient. The calculator works internally in meters but lets you work in either metric or US customary units.

Results Summary

The main result appears below. Quick stats show angle, slope ratio (1 in N), and length along the slope in both meters and feet.

Engineering Reference

Slope Calculator: From Percent Grade to Angle and Run

Learn how to use the slope calculator to move confidently between percent grade, rise, run, and angle. This guide shows you how the equations work, what the outputs mean in the field, and how to spot inputs that don’t make sense before they cause design or construction problems.

8–10 min read Civil, structural & site design

Quick Start: Using the Slope Calculator Without Getting Burned

The slope calculator under this guide is built around the standard definition of slope: \[ S = \frac{\Delta h}{\Delta x}, \quad S(\%) = 100 \cdot \frac{\Delta h}{\Delta x} \] where \(\Delta h\) is the rise (vertical change) and \(\Delta x\) is the run (horizontal distance).

  1. 1 Pick what you want to solve for. In the calculator’s Solve For control, decide whether you need slope (percent grade), rise, or run. Hiding the unknown input keeps the form focused and reduces mistakes.
  2. 2 Set your units before typing numbers. Choose meters vs feet for distance, and let the calculator handle conversions internally. Mixing units is one of the most common sources of bad slopes.
  3. 3 Enter the known values. For a typical workflow:
    • To get slope (%), enter rise and run.
    • To get rise, enter slope (%) and run.
    • To get run, enter slope (%) and rise.
  4. 4 Read the main output carefully. The green result row shows the calculated value in the units you selected, with a clear label like “Slope gradient”, “Rise / vertical change”, or “Run / horizontal distance.”
  5. 5 Use Quick Stats to understand the slope, not just the number. Below the main result, the calculator reports:
    • Slope gradient \(S\) in percent.
    • Angle \(\theta\) in degrees using \(\theta = \arctan(\Delta h/\Delta x)\).
    • Slope ratio as “1 in \(N\)” where \(N = \Delta x / \Delta h\).
    • Length along slope \(L = \sqrt{\Delta x^2 + \Delta h^2}\) in meters and feet.
  6. 6 Toggle “Show Steps” if you need to document the math. The steps section mirrors what you would write in a design calc: normalization to SI units, core equation, angle, ratio, and slope length.
  7. 7 Sanity-check against typical values. A sidewalk at 40% or a storm pipe at 0.0001% should trigger a second look at your inputs, units, and design assumptions.

Tip: For quick field checks, measure rise and run with a tape or level, plug them directly into the slope calculator on your phone, and compare with the design slope from the drawings.

Warning: Do not use length along the slope in place of horizontal run. The calculator reports both, but the equations for grade and drainage are based on horizontal distance.

Choosing Your Method: Survey Data, Plans, or Field Measurements

The same slope calculator works whether you start from elevations, tape-measured distances, or values pulled from drawings. The key is to pick a consistent workflow and stick to it.

Method A — Rise and Run from the Field

This is the most intuitive method for stairs, ramps, small embankments, and short pipe runs. You directly measure vertical and horizontal differences.

  • Easy to explain to contractors and non-engineers.
  • Great for as-built checks and rehab projects.
  • No need to dig through surveying reports.
  • Accuracy depends on how you level and measure.
  • Long slopes are harder to measure without survey equipment.
\(S(\%) = 100 \cdot \dfrac{\Delta h}{\Delta x}\) using measured rise and run.

Method B — Elevation Difference and Plan Distance

Here you start from surveyed elevations or design contours. You compute the rise from elevations and the run from horizontal distances on the plan.

  • Works well at site or corridor scale (roads, channels, pipelines).
  • Elevations and distances are usually already in the design model.
  • Easy to batch through multiple segments.
  • Requires careful unit handling (m vs ft, stationing vs length).
  • Design changes can invalidate earlier slope checks.
\(\Delta h = z_\text{upstream} – z_\text{downstream}, \quad \Delta x = L_\text{horizontal}\).

Method C — Target Slope and One Distance

Often you know the design slope (e.g., 2% for drainage) and one of the distances. The calculator can back-solve the other dimension.

  • Ideal for designing ADA ramps, driveways, and drainage lines.
  • Lets you iterate quickly on “what-if” scenarios.
  • Easy to forget maximum allowable slopes from code or guidelines.
  • Does not automatically check for clearance or headroom issues.
\(\Delta h = \dfrac{S(\%)}{100} \cdot \Delta x \quad\text{or}\quad \Delta x = \dfrac{\Delta h \cdot 100}{S(\%)}\).

What Moves the Number: Key Drivers for Slope Calculations

Slope looks simple, but small changes in inputs can flip a design from compliant to unsafe. Use this section as a checklist when something feels “off.”

Vertical difference \(\Delta h\)

Even a small error in elevations can change grade significantly over short runs. Always confirm which datum and benchmark your survey is using before computing slope.

Horizontal distance \(\Delta x\)

Design drawings may show plan length, while field measurements might follow the slope. The calculator expects horizontal distance for the core slope equations.

Units and rounding

A 0.02 m/m slope equals 2%. Mistyping 0.2 instead of 0.02 adds an order of magnitude. Use the unit selectors and keep one consistent set of units throughout your calculation.

Direction (uphill vs downhill)

The magnitude of slope is usually what matters for drainage and accessibility, but sign conventions (positive uphill, negative downhill) are important in structural and geotechnical analyses.

Regulatory limits

Building codes and road design manuals define maximum slopes for comfort and safety. The slope calculator won’t enforce these automatically, so you still need to compare outputs to your governing criteria.

Surface type & friction

For the same geometric slope, a rough concrete ramp and a smooth metal ramp behave very differently. Use the calculator for geometry, then check friction and surface treatment separately.

Worked Examples: From Numbers to Practical Interpretation

The following examples mirror how you might use the slope calculator in real projects. The exact numeric values you see in the app will match these steps when you enter the same inputs.

Example 1 — Sidewalk Ramp with Maximum Comfortable Slope

  • Scenario: Short sidewalk ramp needed to connect two landings.
  • Elevation difference: \(\Delta h = 0.30\ \text{m}\).
  • Available horizontal space: \(\Delta x = 4.0\ \text{m}\).
  • Objective: Compute percent grade, angle, and slope length.
1
Enter inputs. In the slope calculator, set Solve For = Slope gradient, choose meters, and enter rise = 0.30 m, run = 4.0 m.
2
Compute percent grade. The core equation is:
\[ S(\%) = 100 \cdot \frac{\Delta h}{\Delta x} = 100 \cdot \frac{0.30}{4.0} = 7.5\% \]
3
Compute angle. The angle is:
\[ \theta = \arctan\!\left(\frac{\Delta h}{\Delta x}\right) = \arctan\!\left(\frac{0.30}{4.0}\right) \approx 4.29^\circ \]
4
Compute slope length. The length along the ramp is:
\[ L = \sqrt{\Delta x^2 + \Delta h^2} = \sqrt{4.0^2 + 0.30^2} \approx 4.01\ \text{m} \]
The calculator also reports this value in feet for quick field checks.

A 7.5% slope is noticeable but still manageable for most pedestrians. You would still compare this against any local accessibility criteria before finalizing the design.

Example 2 — Stormwater Pipe Slope from Elevations

  • Scenario: 50 m storm drain line between two manholes.
  • Invert elevations: Upstream \(z_u = 101.40\ \text{m}\), downstream \(z_d = 100.90\ \text{m}\).
  • Horizontal distance: \(\Delta x = 50\ \text{m}\).
  • Objective: Verify that the slope meets minimum self-cleaning criteria.
1
Compute rise from elevations.
\[ \Delta h = z_u – z_d = 101.40 – 100.90 = 0.50\ \text{m} \]
Enter rise = 0.50 m and run = 50 m into the slope calculator.
2
Compute slope in percent and ratio.
\[ S(\%) = 100 \cdot \frac{0.50}{50} = 1.0\% \] \[ N = \frac{\Delta x}{\Delta h} = \frac{50}{0.50} = 100 \quad\Rightarrow\quad \text{slope ratio } 1\text{ in }100 \]
The calculator’s quick stats will show 1.0% and 1 in 100 automatically.
3
Check against criteria. Many small-diameter storm drains require around 0.5–1.0% slope for self-cleaning. Here, 1.0% is within a typical acceptable range, assuming capacity and velocity also check out.

Because the slope calculator clearly reports percent grade, ratio, and angle, you can quickly judge whether the design feels realistic or if the elevations and distances need another pass.

Common Layouts & Variations: Where Slope Numbers Actually Get Used

Different applications expect very different slope ranges. The calculator gives you geometry; use this table to connect those numbers to typical use cases.

ApplicationTypical Slope RangeNotes & Design Considerations
Interior floor drainage1–2% Used near floor drains and wet rooms. Too flat → ponding; too steep → uncomfortable walking and rolling loads.
Accessible ramps / walkways~4–8% (check local codes) Governed by accessibility standards and maximum rise/run rules. Use the slope calculator to iterate ramp length until both grade and run meet code.
Driveways & parking ramps5–15% Lower values improve comfort and traction; steeper segments may require special surfacing, landings, or transition curves.
Roadway longitudinal grade0.3–7% (context-dependent) Arterials, local streets, and high-speed roads all have preferred ranges for safety and drainage. Use the calculator to sanity-check grades along vertical curves and tangents.
Open channels & ditches0.1–3% Too flat and flow may stagnate; too steep and erosion becomes a concern. Hydraulic checks must complement the pure geometric slope.
Gravity pipelines (sanitary/storm)0.1–4%+ Minimum slopes are often specified by diameter for self-cleaning. Use the slope calculator with invert elevations to verify each segment.
Roof slopes2–50%+ Low-slope roofs may be specified as “x in 12” while steep roofs are more naturally described by angle. The calculator can convert between ratio, percent, and degrees.
  • Confirm that your calculated slope falls within the recommended range for the application.
  • Check both minimum and maximum limits from your governing code or standard.
  • Be careful with sign conventions when documenting slopes along a profile.
  • Use multiple points (not just endpoints) when slopes vary along the length.
  • For complex sites, build a small table of station, elevation, and slope using the calculator.
  • Always document which units you used so others can reproduce your results.

Specs, Logistics & Sanity Checks Before You Commit

A slope calculator is most powerful when paired with good engineering judgment. Use these panels as a mental checklist before you send drawings out the door or sign off on as-built measurements.

Spec-Level Checks

  • Compare the calculated slope to the project specifications and code limits.
  • Make sure minimum drainage slopes are met even after construction tolerances.
  • For ramps and stairs, check both individual runs and the overall rise/run ratio.

The calculator helps you compute the numbers; your spec book and code references tell you whether those numbers are acceptable.

Field & Construction Considerations

  • Account for realistic placement tolerances (e.g., ±10 mm in elevation).
  • Check that slab or pipe bedding allows for the required slope along the full length.
  • Verify that transition slopes at tie-ins do not create trip hazards or ponding.

When you re-measure as-built elevations, plug them into the slope calculator to quickly confirm that built slopes match the design intent.

Numerical Sanity Checks

  • If the angle seems extreme, back-calculate the slope ratio and visualize “1 in N”.
  • Try a quick unit change (m ↔ ft) to see if your numbers remain consistent.
  • Cross-check by solving for a different variable (e.g., solve for rise instead of slope).

A short “what-if” loop with the slope calculator often reveals unit typos or sign errors that would otherwise slip through.

As a final step, document both the inputs and outputs you used in the calculator. Screenshots or copied step-by-step text can become part of your design calculation package or field inspection report.

Frequently Asked Questions

What is the formula used by the slope calculator?
The calculator uses the standard geometric definition of slope: \[ S = \frac{\Delta h}{\Delta x}, \quad S(\%) = 100 \cdot \frac{\Delta h}{\Delta x} \] where \(\Delta h\) is the vertical rise (or fall) and \(\Delta x\) is the horizontal run. The same relationship is rearranged to solve for rise or run when you choose those options.
What is the difference between slope, percent grade, and angle?
Slope is the ratio \(\Delta h / \Delta x\). Percent grade is that ratio multiplied by 100, so a slope of 0.05 corresponds to a 5% grade. Angle \(\theta\) is measured from the horizontal and is computed as \(\theta = \arctan(\Delta h / \Delta x)\). The calculator reports all three so you can switch to whichever form your drawings or codes use.
Should I use horizontal run or length along the slope?
For computing percent grade and most drainage checks, you should use horizontal run. Length along the slope is useful for material quantities (like ramp or pipe length) but not for the basic slope equation. The slope calculator reports both values so you can see the distinction clearly.
Can the slope calculator handle negative slopes?
Yes. If you treat uphill as positive and downhill as negative, the underlying math still works. The calculator focuses on the magnitude of slope for reporting percent grade and angle, but you can track direction in your own sign convention and annotations on the profile or plan.
Why does my slope look wrong when I switch units?
Slope is dimensionless, so if you convert both rise and run consistently (e.g., m to ft for both), the ratio should not change. If the slope changes when you switch units, it usually means one value was converted and the other was not, or that you mixed metric and imperial distances in the inputs.
How steep is too steep for a ramp or driveway?
The answer depends on local codes and project type, but many accessibility guidelines cap long ramps around single-digit percent slopes, while driveways may allow steeper values. Use the slope calculator to compute the exact grade, then compare it to the limits in your governing standards rather than relying on a single “rule of thumb.”
Can I use this slope calculator for pipes and channels?
Yes, as long as you remember that the calculator only handles the geometric slope. For hydraulic design you still need to check flow capacity, velocity, and energy grade line using the appropriate hydraulic equations. The output from this slope calculator is the starting point for those additional checks.
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