What is a slope / grade calculator?
This tool converts a rise (vertical change) and a run (horizontal distance) into a slope expressed several useful ways: as a percent grade, as an angle of incline in degrees, as the true slope length (hypotenuse), and as a "1 in N" ratio. It works with any consistent unit — metres, feet, or inches — because grade and angle are dimensionless.
How to use it
Enter the rise and the run using the same units for both, then read the results. The percent grade is the headline figure most commonly used for roads, ramps, roofs and drainage. The angle is handy for construction and trigonometry, while the 1-in-N ratio is widely used for railways and accessibility ramps.
The formula explained
Grade is simply rise divided by run, multiplied by 100: $$\text{grade}\% = \frac{\text{rise}}{\text{run}} \times 100$$ The angle of incline is the arctangent of rise over run: $$\theta = \arctan\!\left(\frac{\text{rise}}{\text{run}}\right)$$ The true slope length follows the Pythagorean theorem: $$L = \sqrt{\text{rise}^2 + \text{run}^2}$$ A 100% grade is a 45° angle, not vertical — a common misconception.
Worked example
A road climbs 3 m over a horizontal distance of 12 m. Grade $$= \frac{3}{12} \times 100 = \mathbf{25\%}$$ Angle $$= \arctan\!\left(\frac{3}{12}\right) = \arctan(0.25) \approx \mathbf{14.04°}$$ Slope length $$= \sqrt{3^2 + 12^2} = \sqrt{153} \approx 12.369 \text{ m}$$ Ratio $$= \frac{\text{run}}{\text{rise}} = \frac{12}{3} = \mathbf{1 \text{ in } 4}$$
FAQ
Is 100% grade the same as straight up? No. 100% grade means rise equals run, which is a 45° angle. A vertical wall would be an infinite grade.
What units should I use? Any, as long as rise and run share the same unit. The percent and angle are unit-independent.
How do I convert grade to angle? Take the arctangent of the grade expressed as a decimal: \(\theta = \arctan(\text{grade}\% / 100)\).
