Slope Calculator (Two Points)

How to use this calculator

Enter the coordinates of two points, (x₁, y₁) and (x₂, y₂). You get the slope, the straight-line distance between the points and the angle of the line.

Formulas

m = (y₂ − y₁) ÷ (x₂ − x₁)
d = √((x₂ − x₁)² + (y₂ − y₁)²)
θ = tan⁻¹(m)

Worked example

Points (1, 2) and (4, 6):

• Rise = 6 − 2 = 4, run = 4 − 1 = 3
• Slope m = 4 ÷ 3 = 1.333
• Distance = √(3² + 4²) = 5
• Angle = tan⁻¹(1.333) = 53.13°

Equation of the line

With the slope, the line is y = m x + c. Find c from either point: c = y₁ − m x₁ = 2 − 1.333 × 1 = 0.667. So y = 1.333x + 0.667.

Slope as grade and angle

Grade	Slope	Angle
1%	0.01	0.57°
5%	0.05	2.86°
10%	0.1	5.71°
100%	1	45°

Wheelchair ramps are commonly limited to about 1:12 (8.3%), or about 4.8°.

Frequently asked questions

What is the slope formula?

m = (y₂ − y₁) ÷ (x₂ − x₁) — the change in y (rise) divided by the change in x (run).

What does a negative slope mean?

The line goes down from left to right. A slope of zero is horizontal; a vertical line has an undefined slope.

How do I turn slope into a percentage grade?

Multiply by 100. A slope of 0.05 is a 5% grade — 5 m rise for every 100 m horizontally.

Embed this calculator