Percent Grade Incline: Formula and Calculation

Calculate percent grade incline by dividing vertical rise by horizontal run and multiplying by 100. Enter the rise and run in the same units to get the slope as a percentage; this calculator also converts that grade to an angle in degrees.

Formula

Percent grade = (vertical rise ÷ horizontal run) × 100. The rise is the vertical change in elevation, and the run is the horizontal distance, measured in the same units. Grade is a ratio expressed as a percentage, not an angle. To convert the same rise-to-run ratio to an angle, use angle = arctan(rise ÷ run); the calculator reports that angle in degrees.

• Rise: vertical elevation change, in metres, feet, or another length unit.
• Run: horizontal distance, in the same length unit as rise.
• Percent grade: rise divided by run, multiplied by 100; expressed as a percentage.
• Incline angle: the angle between the sloping surface and the horizontal, in degrees.

For example, a rise of 1 metre over a horizontal run of 10 metres is a 10% grade. Its angle is about 5.71°, not 10°. The calculation assumes a straight, uniform slope between the two points.

Worked Example

Using the calculator’s default inputs, the vertical rise is 1 m and the horizontal run is 10 m.

1. Divide rise by run: 1 m ÷ 10 m = 0.1.
2. Multiply by 100: 0.1 × 100 = 10% grade.
3. Convert the ratio to an angle: arctan(1 ÷ 10) = arctan(0.1) ≈ 5.71°.

The calculator therefore returns a 10.00% grade and an incline angle of 5.71°. The metres cancel in the division, leaving a dimensionless ratio.

What Percent Grade Means

A 10% grade means the elevation changes by 10 units for every 100 units of horizontal distance. It does not mean the surface rises 10 units along every 100 units measured on the slope itself. Grade is based on horizontal run.

A positive grade describes an uphill rise in the direction being measured. If elevation decreases along that direction, the signed grade is negative; for example, a 2 m drop over a 50 m horizontal run is −4%. This calculator requires nonnegative inputs and reports the magnitude of the incline. To describe a descent as a signed grade, retain the direction separately or record the elevation change as a negative value using a tool that permits signed inputs.

How to Measure Rise and Run

Rise is the difference in elevation between the start and end points. Run is the horizontal distance between their vertical projections—not the length measured along the sloping ground. You can use metres with metres or feet with feet. If measurements use different units, convert one before calculating; otherwise, the ratio will be wrong.

For a short, even ramp, a level and a ruler can help establish the vertical and horizontal distances. For a longer route, elevation readings and a map or surveying measurement may be more suitable. Small errors in either measurement can noticeably affect the result, particularly on shallow slopes where the rise is small compared with the run.

For a route that curves or changes steepness, the result from its total elevation change divided by its total horizontal distance is an average grade. It does not reveal the steepest section. Measure individual sections if local steepness matters.

Examples and Angle Comparison

• 1 m rise over 20 m run: 1 ÷ 20 × 100 = 5% grade; angle ≈ 2.86°.
• 3 ft rise over 100 ft run: 3 ÷ 100 × 100 = 3% grade; angle ≈ 1.72°.
• 1 ft rise over 12 ft run: 1 ÷ 12 × 100 ≈ 8.33% grade; angle ≈ 4.76°.

Percent grade and degrees describe the same slope in different ways, but their numbers are not interchangeable. The conversion is nonlinear: an angle of 45° corresponds to a 100% grade, because its rise equals its horizontal run. A 100% grade is therefore not a vertical wall; a vertical slope has no finite horizontal run, so its grade is undefined or tends toward infinity.

Common Calculation Mistakes and Limits

• Using slope length as run: The denominator must be horizontal distance. Distance measured along the incline is longer, so using it gives a different, incorrect grade.
• Mixing units: Convert feet to metres, inches to feet, or other mismatched units before dividing.
• Confusing 10% with 10°: A 10% grade is about 5.71°. Use the angle output when a question specifically asks for degrees.
• Rounding too early: Keep unrounded measurements through the calculation, then round the final result to a sensible precision. Extra decimal places cannot correct inaccurate field measurements.

The formula gives geometric steepness only. It does not determine a route’s difficulty, travel time, traction, drainage, accessibility, or suitability for a particular use. Those depend on factors beyond the rise and run, such as surface, length, weather, and changing conditions.

Frequently Asked Questions

How do I calculate percent grade from rise and run?
Divide the vertical rise by the horizontal run, then multiply by 100. If both are measured in the same units, those units cancel.

Is a 10% slope the same as 10 degrees?
No. A 10% grade corresponds to an angle of about 5.71°. Percent grade is rise divided by horizontal run; degrees measure the angle from horizontal.

What does a 5% grade mean?
It means the elevation changes by 5 units for every 100 units of horizontal distance. For instance, a 5 m rise over a 100 m run is 5%.

Can percent grade be over 100%?
Yes. If the vertical rise is greater than the horizontal run, the grade exceeds 100%. A 2 m rise over a 1 m horizontal run is 200%, equivalent to an angle of about 63.43°.

Should I use horizontal distance or the distance along the slope?
Use horizontal distance. The standard percent-grade formula divides vertical rise by horizontal run, not by the sloping surface length.

How do I calculate the grade of a route with changing slopes?
Using total elevation change divided by total horizontal distance gives the route’s average grade. To find local steepness, calculate separate grades for the sections you want to compare.

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in rise | Vertical rise | m | 1 | 0
in run | Horizontal run | m | 10 | 0
out grade | Percent grade | % | 100 * rise / run | 2
out angle | Incline angle | degrees | atand(rise / run) | 2