“Gradient” is the UK word for slope. It describes steepness: hills, roofs, ramps and graphs of rates. A gradient of 0.5 means 1 up for every 2 across.
How to use the Gradient Calculator
- Point 1 – x
- Point 1 – y
- Point 2 – x
- Point 2 – y
Results update as you type, and everything is calculated in your browser.
How it works
The rise and run are the differences in y and x. The angle is the arctangent of the gradient; the distance uses the Pythagorean theorem.
Tips
- Sketch the points first – a quick drawing shows whether a slope should be positive or negative.
- Keep the order of the points consistent in every formula.
- Vertical lines have an undefined slope; horizontal lines have slope zero.
- Use the same units on both axes when you measure distances or angles.
Common mistakes to avoid
- Swapping x and y coordinates.
- Subtracting the coordinates in a different order in the numerator and denominator of the slope.
- Forgetting that the distance is always positive.
Inputs explained
| Field | What to enter |
|---|---|
| Point 1 – x | A number |
| Point 1 – y | A number |
| Point 2 – x | A number |
| Point 2 – y | A number |
What each result means
- Gradient = ([Point 2 – y] – [Point 1 – y])÷([Point 2 – x] – [Point 1 – x])
- Rise = [Point 2 – y] – [Point 1 – y]
- Run = [Point 2 – x] – [Point 1 – x]
- Angle of inclination = deg(atan2([Point 2 – y] – [Point 1 – y], [Point 2 – x] – [Point 1 – x]))
- Distance between the points = sqrt(([Point 2 – x] – [Point 1 – x])^2 + ([Point 2 – y] – [Point 1 – y])^2)
- Gradient as a percentage = ([Point 2 – y] – [Point 1 – y])÷([Point 2 – x] – [Point 1 – x])×100
Example values
How the main result changes when Point 1 – x changes and everything else stays at the example values above:
| Point 1 – x | Gradient |
|---|---|
| 0.5 | 0.4615 |
| 0.75 | 0.48 |
| 1 | 0.5 |
| 1.25 | 0.5217 |
| 1.5 | 0.5455 |
| 2 | 0.6 |
Formula
Gradient m = rise ÷ run = (y₂ − y₁) ÷ (x₂ − x₁)Worked example
Inputs — Point 1 – x: 1; Point 1 – y: 2; Point 2 – x: 7; Point 2 – y: 5.
Results — Gradient = 0.5; Rise = 3; Run = 6; Angle of inclination = 26.5651 °; Distance between the points = 6.70820393; Gradient as a percentage = 50 %.
Key terms
- Gradient
- The steepness of a line, rise over run.
Frequently asked questions
How do I find a gradient from two points?
Divide the change in y by the change in x.
What does a negative gradient mean?
The line goes down from left to right.
What is the gradient of a vertical line?
Undefined, because the run is zero.
Is gradient the same as slope?
Yes, in coordinate geometry.
What formula does the Gradient Calculator use?
Gradient m = rise ÷ run = (y₂ − y₁) ÷ (x₂ − x₁).