Right Triangle Calculator guide
Right Triangle Calculator: Sides, Angles and SOH CAH TOA
Use our right triangle calculator to find all the sides and angles of a right-angled triangle from two sides or a side and an angle.
By the AllCalculator editorial teamUpdated 16 October 20261 min read
A right-angled triangle has one 90° angle, which makes it easy to solve with Pythagoras and trigonometry. Our Right Triangle Calculator finds everything from just two values.
How to use the calculator (Right Triangle Calculator)
- Choose what you know: both shorter sides, a side and the hypotenuse, a side and an angle, or the hypotenuse and an angle.
- Enter the values.
You'll see all three sides, all three angles, the area, perimeter and the height to the hypotenuse.
SOH CAH TOA
For angle A, with side a opposite it, side b next to it and hypotenuse c:
- sin A = opposite ÷ hypotenuse = a ÷ c
- cos A = adjacent ÷ hypotenuse = b ÷ c
- tan A = opposite ÷ adjacent = a ÷ b
The two smaller angles always add up to 90°.
A worked example
With the calculator's default settings, shorter sides of 3 and 4:
- Hypotenuse: √(9 + 16) = 5
- Angle A: tan⁻¹(3 ÷ 4) = 36.87°
- Angle B: 90° − 36.87° = 53.13°
- Area: ½ × 3 × 4 = 6
Frequently asked questions
How do I find the angle of a slope or ramp?
Enter the rise as side a and the horizontal run as side b. Angle A is the slope angle.
What's the height to the hypotenuse?
It's the perpendicular distance from the right angle to the hypotenuse: a × b ÷ c.
What if there's no right angle?
Use our Triangle Calculator, which works for any triangle.
Sources and further reading
- GOV.UK: National curriculum in England – mathematicsgov.uk
- Wolfram MathWorld: Right trianglemathworld.wolfram.com
Links open official and independent websites in a new tab.
This guide is general information to help you understand your options. It isn't financial, tax, legal or building advice and doesn't take your personal circumstances into account. Figures were checked when the guide was last updated and can change, so confirm anything important with GOV.UK, HMRC, a regulated adviser or a qualified tradesperson.