Slope, pitch, and grade formulas
Slope describes both the steepness and direction of a line or surface. Mathematically, slope m = Rise / Run = Δy / Δx = (y2 − y1) / (x2 − x1).
Grade percentage is calculated as Grade % = (Rise / Run) × 100%. A 100% grade corresponds to a 45° angle (Rise = Run).
The angle of inclination θ is found using trigonometry: θ = arctan(Rise / Run). The hypotenuse length (travel distance along the slope) is found with Pythagoras: d = √(Rise² + Run²).
Worked example: Ramp gradient
An access ramp with a vertical rise of 0.5 metres and a horizontal run of 10 metres has:
Slope = 0.5 ÷ 10 = 0.05. Percentage grade = 0.05 × 100 = 5.0%.
Angle = arctan(0.05) ≈ 2.86°. In British ratio terminology, this is a 1 in 20 slope.
Inputs for the slope calculator
Rise and Run
Enter vertical change (rise) and horizontal distance (run) using the same measurement unit.
CALCULATOR QUESTIONS
Slope, pitch & grade calculator questions
What is a 100% slope?
A 100% slope means the vertical rise equals the horizontal run (e.g. 1 metre rise for every 1 metre run), corresponding to an angle of 45 degrees.
How do you convert pitch to degrees?
For a US pitch of X in 12, calculate arctan(X / 12) × (180 / π). For example, a 4/12 pitch is arctan(4/12) ≈ 18.43 degrees.