Slope calculator: rise, run and angle

Calculate slope from two points or rise and run. Convert between percent grade and degrees and explore the triangle with intermediate calculations.

Mode

Rise

Horizontal run

Results update as you type.

Result

100% is not vertical

A rise equal to the horizontal run gives 100% and 45°. Try 100% and then 90° to see the difference.

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How to use it

Choose one of four modes. Use a decimal point or comma; results update immediately. Keep lengths in the same unit. Percent and angle modes show a normalised ramp. Presets load uphill, downhill and vertical cases. Copy results includes displayed measurements; Reset restores a rise of 10 and run of 100.

Drag the blue handle. With points or rise and run it changes the vertical coordinate; with degrees or percent it rotates the ramp.

Use arrow keys on the handle; Shift increases the step. You can also type the value.

Method

Slope is rise divided by horizontal run. Multiplying by one hundred gives percent grade; arctangent gives the angle. Vertical lines have undefined slope.

m = \frac{Δy}{Δx}

p = 100 \times m

α = \arctan (m)

Reading the result

A 100% grade equals 45°, not 90°. Negative slope falls as x increases. Rise is vertical and run is horizontal, not the length of the ramp.

Worked example

A rise of 10 over a horizontal run of 100 gives 10%, or about 5.71°. The sloping length is about 100.50 in the same unit. Load the example to compare the three measurements in the drawing.

Input: $\frac{10}{100}$
Result: $10 %; ≈ 5.71 °$

Calculation steps

Slope coefficient
$\frac{10}{100} = 0.1$
Grade (%)
$0.1 \times 100 = 10$

Slope is rise divided by horizontal run. Multiplying by one hundred gives percent grade; arctangent gives the angle. Vertical lines have undefined slope.

Limits and data handling

Points must differ. Angles range from −90° to 90°; numeric inputs have absolute value at most 10¹². Results are numerical approximations, not engineering assessments.

Processing takes place in your browser. The tool does not save the values you enter.

Sources

OpenStax — Slope

Frequently asked questions

Does 100% mean 90 degrees?

A 100% grade equals 45°, not 90°. Negative slope falls as x increases. Rise is vertical and run is horizontal, not the length of the ramp. Processing takes place in your browser. The tool does not save the values you enter.