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Slope calculator

This slope calculator works out the slope from rise and run – or converts between percent, degrees and ratio. A rise of 1.2 over a run of 15 is an 8% slope, which equals 4.57° and a ratio of 1 : 12.5.

Example: What is given: Rise and horizontal run · Rise (height difference) 1.2 · Horizontal run 15 · Horizontal distance for the rise (optional) 10 → Slope: 8 %. Source: Wikipedia – Grade (slope): percent grade, angle and ratio. Updated: .

any unit, but the same as for the run
measured level, not along the slope
e.g. length of a path or ramp
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Result

Slope
8 %
Angle
4.57°
Ratio
1 : 12.5
Over the distance
Over a horizontal distance of 10: 0.8 rise, 10.03 along the slope (in the unit you entered).
Calculation
Slope = rise ÷ run × 100 = 1.2 ÷ 15 × 100 = 8%
Comparison table
PercentDegreesRatio
1 %0.57°1 : 100
2 %1.15°1 : 50
3 %1.72°1 : 33.33
5 %2.86°1 : 20
6 %3.43°1 : 16.67
8 %4.57°1 : 12.5
10 %5.71°1 : 10
12 %6.84°1 : 8.33
15 %8.53°1 : 6.67
20 %11.31°1 : 5
25 %14.04°1 : 4
30 %16.7°1 : 3.33
40 %21.8°1 : 2.5
50 %26.57°1 : 2
75 %36.87°1 : 1.33
100 %45°1 : 1

How it is calculated

Slope: the formulas

Slope in percent = rise ÷ horizontal run × 100. The angle follows from the arctangent: α = arctan(percent ÷ 100). In reverse, percent = tan(α) × 100. For a ratio of 1 : n, percent = 100 ÷ n.

Percent is not degrees

Percent refers to the horizontal distance, not to the slope length. 100% is therefore 45°, not 90°. For small slopes a rule of thumb is degrees ≈ percent × 0.57: 10% is about 5.7°.

Rise and slope length

If the horizontal distance is known, the rise is distance × percent ÷ 100 and the length along the slope is distance × √(1 + (percent ÷ 100)²). At 8% over 10, that is a rise of 0.8 and a slope length of 10.03.

Downhill grade

A downhill grade is calculated the same way, just going down: an 8% grade means the ground drops 8 for every 100 of horizontal distance.

Honest limits

The calculator only converts quantities and names no limits. Permitted slopes for ramps, stairs, roofs or roads are set in standards and building codes; the version that applies to your project is decisive.

Frequently asked questions

How do I calculate slope as a percentage?

Divide the rise by the horizontal run and multiply by 100: 1.2 ÷ 15 × 100 = 8%.

How do I convert percent slope to degrees?

With the arctangent: angle = arctan(percent ÷ 100). 10% is 5.71°, 100% is 45°.

How do I convert degrees to percent slope?

Percent = tan(angle) × 100. 30° is 57.74%, 45° is 100%.

What does a ratio of 1 : 12 mean?

1 unit of rise for every 12 units of horizontal run: 100 ÷ 12 = 8.33% or 4.76°.

How much rise is an 8% slope over 100?

8. The rise is the horizontal distance times percent ÷ 100.

Sources and legal basis

As of: · Editorial policy

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