Slope percentage and angle in degrees are not the same measurement — a 100% slope is a 45-degree incline, not vertical, a mix-up that trips up a lot of people.
How it works
Dividing the rise (vertical change) by the run (horizontal distance) and multiplying by 100 gives the slope percentage; taking the arctangent of that same ratio gives the angle in degrees.
What this does not include
This does not include a slope expressed as a ratio (like “1 in 12”), a common alternative format for wheelchair ramp specifications — this calculator outputs percentage and degrees only.
How to use this calculator
- Enter the rise (vertical change) and run (horizontal distance).
A worked example
A rise of 5 over a run of 20: slope percentage = 5/20 × 100 = 25%, angle ≈ 14.04°.
A rise of 20 over a run of 20: slope percentage = 100%, angle = 45° — a common point of confusion, since 100% slope means a 45° angle, not vertical.
What the variables mean
| Variable | Meaning |
|---|---|
| Rise | Vertical change |
| Run | Horizontal distance |
Edge cases worth knowing
A 100% slope is a 45° angle, not vertical. Slope percentage and angle scale very differently — doubling the percentage doesn’t double the angle, since the relationship is a tangent, not a linear one.
A run of zero makes the slope percentage undefined — a purely vertical rise with no horizontal run isn’t expressible as a percentage slope.
Frequently asked questions
Why isn’t a 100% slope vertical?
Because slope percentage is rise divided by run, not an angle measurement directly — a 100% slope means the rise equals the run, which works out to a 45-degree angle, not 90 degrees.
Where is slope percentage commonly used?
Road grades, wheelchair ramp specifications, roof pitch, and hiking trail difficulty ratings are all commonly expressed as a slope percentage.
Can slope percentage exceed 100%?
Yes — any slope steeper than a 45-degree angle produces a slope percentage above 100%, since the rise exceeds the run at that point.
