Rise Over Run Calculator — Slope, Grade & Angle
Find the slope, angle and percent grade of any line or ramp. Enter the rise (vertical change) and run (horizontal change), or type in two coordinate points, and get the slope as a decimal, the angle in degrees and the gradient as a percentage.
Input method
Positive = uphill left-to-right, negative = downhill, zero = flat
- 1
Slope
rise ÷ run = 3 ÷ 4 = 0.75 - 2
Angle from horizontal
arctan(0.75) = 36.87Angle the line makes with the horizontal, in degrees.
How does this calculator work?
Slope = rise ÷ run (vertical change divided by horizontal change). If you have two points (x₁, y₁) and (x₂, y₂), slope = (y₂ − y₁) ÷ (x₂ − x₁). Multiply by 100 for percent grade; take the inverse tangent for the angle in degrees.
Formula
How this is calculated
Slope is the ratio of how much a line rises (moves vertically) for each unit it runs (moves horizontally). A slope of 0.75 means the line goes up 0.75 units for every 1 unit across; a slope of −1 means it descends one unit for each unit you travel right. When the run is zero, the line is perfectly vertical and the slope is mathematically undefined.
From two coordinate points (x₁, y₁) and (x₂, y₂) the rise is y₂ − y₁ and the run is x₂ − x₁, giving slope m = (y₂ − y₁) ÷ (x₂ − x₁). The angle is the inverse tangent of the slope: θ = arctan(m), measured in degrees from the horizontal. Percent grade, used for roads and ramps, is simply slope × 100 — a 6% grade road rises 6 m per 100 m of horizontal distance.
The 1 : n ratio (1 unit up for every n units across) is the reciprocal of the absolute slope and is the standard expression for roof pitches and construction slopes.
Frequently asked questions
ADA guidelines in the US require a maximum slope of 1:12 (8.3%, ≈ 4.76°) for wheelchair ramps. Steeper temporary ramps up to 1:8 (12.5%, ≈ 7.13°) are allowed in some cases when space is constrained.
A road grade is the percent slope: a 5% grade rises 5 m for every 100 m of horizontal distance. Highways are typically 4–6% maximum; mountain roads can reach 8–12%. The sign "6% grade" on a highway means 6 units up per 100 units across.
A negative slope means the line falls from left to right (as x increases, y decreases). For example, a slope of −0.5 drops 0.5 units for each 1 unit you move to the right.
Also known as
TG we-Calculate Editorial Team. (2026). Rise Over Run Calculator — Slope, Grade & Angle [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/rise-over-run-calculator
TG we-Calculate Editorial Team. "Rise Over Run Calculator — Slope, Grade & Angle." TG we-Calculate. 2026. https://we-calculate.com/calculator/rise-over-run-calculator.
TG we-Calculate Editorial Team, "Rise Over Run Calculator — Slope, Grade & Angle," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/rise-over-run-calculator
@misc{wecalculate_rise_over_run_calculator, title = {Rise Over Run Calculator — Slope, Grade & Angle}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/rise-over-run-calculator}}, year = {2026}, note = {TG we-Calculate} }
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