Angle Size Calculator
Choose which two sides of a right triangle you know and enter them. The calculator finds the angle, the other angle, the missing side and the slope as a percentage and a ratio.
- Any two sides
- Degrees and radians
- Slope and gradient
Opposite is across from the angle, adjacent is next to it, and the hypotenuse is the longest, sloping side.
Two sides of a right triangle fix its angles. Use tangent when you know the rise and run, sine when you know the rise and the sloping side, and cosine for the run and sloping side. It is how builders set roof pitches, ramps and stairs without a protractor.
Angle and slope chart
Rise over run. Search for an angle.
| Angle | Slope % | Ratio | Rise per 1 m |
|---|---|---|---|
| 1° | 1.7 | 1 in 57 | 17 mm |
| 5° | 8.7 | 1 in 11.4 | 87 mm |
| 10° | 17.6 | 1 in 5.7 | 176 mm |
| 15° | 26.8 | 1 in 3.7 | 268 mm |
| 22.5° | 41.4 | 1 in 2.4 | 414 mm |
| 30° | 57.7 | 1 in 1.7 | 577 mm |
| 35° | 70 | 1 in 1.4 | 700 mm |
| 45° | 100 | 1 in 1 | 1,000 mm |
| 60° | 173 | 1 in 0.58 | 1,732 mm |
Slope % is rise ÷ run × 100. A 1 in 12 ramp is 8.3% and 4.8°.
Rise and angle
Over a run of 100. Slide the rise.
Angle does not grow evenly with rise. The first 50 of rise gives 27°, the next 50 only adds 18° more.
How to find an angle
SOH CAH TOA. Step through it.
Name the sides
Opposite, adjacent, hypotenuse.
Calculators need to be in degree mode for these, or the answer comes out in radians.
Sine, cosine or tangent
Which ratio to use. Compare them.
Opposite ÷ adjacent. Rise over run.
Opposite ÷ hypotenuse.
Adjacent ÷ hypotenuse.
Tangent is the most used on site, because rise and run are the easiest to measure.
Setting out an angle
On site. Tick each item.
Tick each item as you go.
A 3-4-5 triangle gives a perfect right angle. Measure 3 along one side, 4 along the other and the diagonal should be 5.
What you get
The whole triangle. Each tile explains one result.
Degrees.
90° minus.
For maths.
By Pythagoras.
Percent and ratio.
Slope as a ratio, such as 1 in 12, is the common way to describe ramps and drains.
Frequently Asked Questions
No question matches that search.
How do I find an angle from two sides?
Use tan⁻¹(opposite ÷ adjacent), sin⁻¹(opposite ÷ hypotenuse) or cos⁻¹(adjacent ÷ hypotenuse).
What angle is a 3-4-5 triangle?
About 36.87° and 53.13°.
How do I convert slope % to degrees?
Angle = tan⁻¹(slope ÷ 100). 10% is 5.7°.
What is a 1 in 12 slope in degrees?
About 4.76°.
What angle is a 45° roof pitch?
Equal rise and run, a slope of 100%.
How do I convert degrees to radians?
Multiply by π ÷ 180.
What is SOH CAH TOA?
A memory aid: Sine = O/H, Cosine = A/H, Tangent = O/A.
Any angle from two sides
Measure two sides, pick the ratio and get the angle. With the slope and missing side shown as well, you have everything you need to set out a roof, ramp or stair.
More size calculators
Each one has its own calculator, worked examples and answers to common questions.