Slope calculator
Slope in per cent and degrees from rise and run.
Fill in the fields and the result will appear here automatically.
Gradient is vertical change divided by horizontal change, expressed as a percentage. It is not degrees: 100% corresponds to 45°, and 15% to about 8.53°. This calculator also gives a signed angle between −90° and 90° and the geometric segment length. Both changes are in metres and may be signed; reversing both signs leaves the same line gradient. Length is non-negative.
How it works
Formula and logic
Slope = rise ÷ run × 100 per cent. The angle is the arctangent of that ratio, and the length is the hypotenuse of rise and run.
Example
A rise of 1.2 m over 8 m is a 15% slope, 8.531 degrees, with a slope length of 8.089 m.
Fields and units
- Rise — m
- Run — m
How to use
- — Enter vertical change in metres: positive upward, negative downward.
- — Enter horizontal change in metres, not distance along the incline. It must be nonzero.
- — A negative run reverses horizontal direction; the ratio of both changes determines the slope sign.
- — Use the hypotenuse as geometric segment length. Standards, allowances and structural suitability require other data.
Method and limitations
- Calculation method
- Formula and logic
- Data or methodology source
- OpenStax: sine and tangent in a right triangle
- Limitation
- One straight segment in a vertical plane with nonzero horizontal change. The angle arctan(rise/run) describes line inclination, not a travel bearing. The formula does not assess building standards or accessibility; inputs are fixed in metres.
FAQ
How do per cent and degrees relate?
p = 100tan(α), with α = arctan(p/100) converted to degrees. For example, 5% ≈ 2.862°, 10% ≈ 5.711° and 100% = 45°. Small-angle linearization applies to radians, not equality of percentage and degree numbers.
What slope is acceptable for a wheelchair ramp?
This page calculates geometry and does not establish whether a ramp is permissible. Requirements depend on jurisdiction, building use, rise, landings and other parameters. The ratio 1:12 is mathematically 8.333…%, not exactly 8%. Check the applicable requirement separately.
Should the run be measured horizontally or along the ground?
Horizontally. Measuring along the incline gives the slope length instead, and using it as the run understates the gradient.
Can the rise be negative?
Yes. The percentage and angle follow the sign of rise/run. With positive run, negative rise gives negative results; when both are negative, the ratio, percentage and angle are positive. For example, −1/−1 gives 100% and 45°.