A slope of 8% is the fraction 2/25. It rises 2 units for every 25 you move horizontally. To find it, divide the rise by the run, and write the result as a ratio, as a fraction or as a percent.
Key facts
- Slope = rise ÷ horizontal run.
- The percent is that fraction multiplied by 100.
- A 10% grade road sign means 10 ft of rise for every 100 ft measured horizontally.
- The ratio 1 : 12 is the fraction 1/12, which is about 8.33% (rounding changes it by less than 0.01 percentage points).
- A 100% slope is 45°, never 90°.
What slope measures
Slope compares two lengths: how much the ground rises and how far it moves horizontally. The run is the horizontal distance, the one you would measure on a plan seen from above, not the length of the sloped surface. Two ramps with the same fraction have the same steepness even if one is long and the other short.
In the triangle, the rise is the vertical leg and the run is the horizontal leg. The hypotenuse is the sloped length and plays no part in the slope.
How to convert a slope from a ratio to a fraction and a percent
The ratio “rise : run” becomes a fraction when you put the rise on top and the run on the bottom. Then you simplify it with the GCF (greatest common factor, also called GCD or HCF) of the two numbers. The ratio to fraction calculator does that conversion, and the ratio simplifier shows the common divisor.
To get the percent, multiply the fraction by 100. In reverse, a percent is a fraction with denominator 100: 8% = 8/100 = 2/25, after dividing both terms by 4. The fraction to percent calculator and the percent to fraction calculator let you check the result.
When the division does not end, the fraction keeps the full value and the percent rounds it. For example, 1/12 × 100 = 25/3, which is 8.333…%.
Worked example: a trail section that rises 18 ft over 240 ft
A trail gains 18 ft of height over 240 ft of horizontal run. What is its slope as a fraction and as a percent?
- Write the ratio. The rise is 18 and the run is 240, both in feet: 18 : 240.
- Simplify. The GCF of 18 and 240 is 6, so 18/240 = 3/40.
- Convert to a decimal. 3 ÷ 40 = 0.075.
- Multiply by 100. 0.075 × 100 = 7.5%.
Result: the slope is 3/40, which is 7.5%.
Check: 7.5% of 240 ft is 0.075 × 240 = 18 ft, the rise you started with.
The same fraction works for a 1 : n ratio. Divide the run by the rise: 240 ÷ 18 = 13.33…, so the trail rises 1 ft for about every 13.3 ft (rounded to tenths). If the quotient is not exact, it is better to leave it as 3 : 40.
Table of common slopes
| Ratio | Fraction | Percent | Angle |
|---|---|---|---|
| 1 : 12.5 | 2/25 | 8% | ≈ 4.57° |
| 1 : 12 | 1/12 | ≈ 8.33% | ≈ 4.76° |
| 1 : 10 | 1/10 | 10% | ≈ 5.71° |
| 1 : 5 | 1/5 | 20% | ≈ 11.31° |
| 1 : 1 | 1/1 | 100% | 45° |
The percent grows faster than the angle: from 10% to 20% the angle goes from 5.71° to 11.31°, but from 20% to 100% it only reaches 45°. Percents and angles are rounded to two decimal places, except 45°, which is exact.
A 10% road sign and a 6 : 12 roof
A 10% grade sign announces 10 ft of rise for every 100 ft of horizontal run, which is the fraction 1/10. It does not mean the road climbs 10 ft in every 100 ft of pavement. Over a horizontal stretch of 250 ft, the rise is 250 × 10/100 = 25 ft, which you can solve with a rule of three.
Roofs are usually given as rise : run. A 6 : 12 roof rises 6 units for every 12 of horizontal run, that is, 6/12 = 1/2 = 50%. The first number is the rise, so an 8 : 12 roof is steeper than a 4 : 12 roof. To see how ratios and proportions relate, there is a guide to ratio, proportion and fraction, and for scale drawings, another on fractions and scales.
From percent to degrees
To get to degrees you need the tangent. In a right triangle, the tangent of the angle is the opposite leg divided by the adjacent leg, that is, rise ÷ run: the same fraction as the slope. So the angle is arctan(rise ÷ run). With a 10% slope, arctan(0.1) ≈ 5.71° (rounded to two decimal places). The guide to fractions of a turn and angles explains how angles are measured with fractions.
Slope describes steepness but does not say whether it is allowed: limits for ramps, roofs and roads depend on the place and the project, and this guide does not cover them.
Sources
The definition of slope as the ratio of the vertical change to the horizontal change, its relation to the tangent of the angle of inclination, and the description of road steepness as a percentage, with 100% corresponding to 45°, appear in the Wikipedia article Slope (accessed October 17, 2026).