Slope Percentage Calculator — Grade, Angle & Ratio
Convert any slope expression — rise/run, decimal ratio, angle in degrees, or percentage grade — into all other forms instantly. Covers uphill and downhill slopes and shows the equivalent right-triangle geometry.
Input type
Very steep (> 15%)
- 1
Rise ÷ run ratio
5 ÷ 20 = 0.25 - 2
Slope percentage
0.25 × 100 = 25Multiply the ratio by 100 to express it as a percentage grade.
How does this calculator work?
Slope % = (rise / run) × 100. A 1:4 rise-to-run ratio equals 25% grade and an angle of ≈14°. Enter any of the four forms — rise/run, ratio, angle, or percent — and all others are computed instantly via tan and arctan. Hypotenuse per unit run = √(1 + ratio²).
Formula
How this is calculated
Slope percentage (also called "percent grade") is the most common way to express how steep a road, ramp, roof, or terrain feature is in engineering and surveying. A 10% grade means you rise 10 units vertically for every 100 units of horizontal distance — not along the slope itself. It is related to the angle of inclination θ by: percent = 100 × tan(θ), and to the simple rise-over-run ratio by percent = ratio × 100.
This calculator accepts four different inputs and converts between all forms. Starting from rise and run, it computes percent, angle (degrees), angle (radians) and the length of the hypotenuse per unit of run. Starting from an angle, it derives the ratio by taking the tangent. Negative slopes (downhill) are handled correctly: a −15% grade descends 15 m per 100 m horizontal.
Limitations: the formula applies to planar, uniform slopes only. Road design standards (AASHTO, EN 13201) specify maximum grades — typically 6–8% for highways, up to 12% for minor roads, and 1:12 (8.33%) for ADA-compliant ramps. Roof pitch is often expressed differently (as X:12 in the US), where X is the rise per 12 units of run; divide by 12 and multiply by 100 to convert to percent.
Frequently asked questions
Slope percentage is rise ÷ run × 100, measured on the horizontal. Slope angle θ is the arctan of the ratio, measured from horizontal. A 45° slope equals 100%, not 45% — they only happen to be close at small angles where tan(θ) ≈ θ in radians.
Most highway design standards limit grades to 6–8%. Collector streets may reach 10–12%. Anything above 15% is considered very steep and rarely used in road design. Mountain roads can exceed 20%, but these are exceptional and usually short.
Divide the rise by the run: 6/12 = 0.5, then multiply by 100 = 50% slope. The angle is arctan(0.5) ≈ 26.6°.
Also known as
TG we-Calculate Editorial Team. (2026). Slope Percentage Calculator — Grade, Angle & Ratio [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/slope-percentage-calculator
TG we-Calculate Editorial Team. "Slope Percentage Calculator — Grade, Angle & Ratio." TG we-Calculate. 2026. https://we-calculate.com/calculator/slope-percentage-calculator.
TG we-Calculate Editorial Team, "Slope Percentage Calculator — Grade, Angle & Ratio," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/slope-percentage-calculator
@misc{wecalculate_slope_percentage_calculator, title = {Slope Percentage Calculator — Grade, Angle & Ratio}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/slope-percentage-calculator}}, year = {2026}, note = {TG we-Calculate} }
Did this calculator help you?