Slope calculator: percent grade, degrees and roof pitch

Work out a slope from any two values

A slope can be written as a percent grade, an angle in degrees, a 1:n ratio, a roof pitch such as 6/12, or inches per foot. This calculator converts between all of them and fills in the missing sides of the triangle: rise, horizontal run and slope length. Separate modes handle roofs, accessibility ramps, road climbs and drain pipes, and a drawing shows the triangle to scale. Imperial units are selected by default; switch to "Metric" if you work in meters.

How to use it

1. On the "Slope" tab, fill in any two of "Rise (height)", "Horizontal run", "Slope length", "Grade in %", "Angle in degrees" and "Ratio 1:n (n)". The rest turn green with the calculated values.
2. To convert a slope, one box is enough: type 30 in "Angle in degrees" and read 57.735%.
3. Pick the length unit (feet, inches, meters…) from the list.
4. The "Roof", "Accessibility ramp", "Road and bike" and "Drainage" tabs ask the questions that matter in each case. "Calculation steps" shows every formula.

Percent grade, degrees and ratio are not the same

Percent grade is rise divided by run, times 100. A rise of 1 ft over a 10 ft run is a 10% grade. The angle is arctan(1 ÷ 10) ≈ 5.711°, the slope length is √(1² + 10²) ≈ 10.050 ft and the ratio is 1:10.

The common mistake: 100% grade is 45°, not 90°. At 100% you rise one foot for every foot forward, the diagonal of a square. A vertical wall would have an infinite grade, so the tool refuses 90°. Going the other way, 30° is 57.735%, and a 1:12 ramp is 8.333%, or 4.764°.

Roof pitch, rafter length and roof area

In the US, roof pitch is the rise in inches for 12 inches of run. A 6/12 pitch is 6 ÷ 12 = 50%, or 26.565°. On the "Roof" tab, enter the pitch, then the footprint of one plane seen from above: its length along the eave and its horizontal width to the ridge. For a plane 30 ft long and 12 ft wide at 6/12, the rafter length is 12 × √(1 + 0.5²) ≈ 13.416 ft and the area is 30 × 13.416 ≈ 402.49 sq ft, about 4.02 roofing squares. Minimum pitch depends on the roofing material and your local code, so check the manufacturer's instructions or ask a roofer.

Ramp slope for wheelchair access

US accessibility standards set a maximum running slope of 1:12 for ramps: every inch of rise needs at least 12 inches of run. A 30 in rise therefore needs 360 in, or 30 ft, of horizontal length. Landings, width and handrails have their own rules, so always check the current official standards and your local code before building.

Road grades and hill signs

Hill warning signs often carry a grade plaque such as 6%. For a climb of 1,000 ft over 2 miles of road, the quick estimate 1,000 ÷ 10,560 gives 9.47%. A bike computer measures distance along the road, though, not horizontally. The horizontal distance is √(10,560² − 1,000²) ≈ 10,512.5 ft, so the true average grade is about 9.512%. The tool shows both.

Drain pipe slope

Drain lines are usually sloped at a fraction of an inch per foot. A slope of 1/4 in per foot is 2.083%; over 20 ft of pipe that means a 5 in drop. On the "Drainage" tab, enter two of the three values and the third is calculated. Fractions such as 1/4 are accepted.

Frequently asked questions

How do I convert percent grade to degrees?

Divide by 100 and take the arctangent: 15% gives arctan(0.15) ≈ 8.531°. The other way, grade = tan(angle) × 100.

Why isn't 100% grade 90 degrees?

Because 100% means the rise equals the run, which is 45°. At 90° the run would be zero.

What does a 1:12 ratio mean?

One unit of rise for twelve units of horizontal run: 1 ÷ 12 ≈ 8.333%.

Are my values saved?

Yes, on this device only. "Clear all" removes them.