Right Triangle Calculator
Solve a complete right triangle from any two known values: sides, angles, area, height, inradius, and circumradius.
Details
Hypotenuse (c)
5
Area
6
Distance around it
12
Height to the long side
2.4
Longest side
5
This solves a right-angled triangle from any two known values: two sides, or a side and an angle.
It returns every remaining side and angle, plus the area and perimeter, and shows which rule it used to get there.
What makes a triangle right-angled
A right triangle has one angle of exactly 90°. That single fact makes it the easiest triangle to solve and the most useful one in practice.
The side opposite the right angle is the hypotenuse, and it is always the longest. The other two are the legs.
Because one angle is already known, you only need two more values to find everything else. With two sides, use Pythagoras. With a side and an angle, use trigonometry.
Opposite and adjacent are defined relative to the angle you are working with, so they swap when you switch angles. The hypotenuse never changes.
What to enter
- Known values
- Which two you have: two legs, a leg and the hypotenuse, or a side and an angle.
- Legs a and b
- The two sides that meet at the right angle.
- Hypotenuse c
- The long side opposite the right angle. It must be longer than either leg.
- Angle A or B
- Either non-right angle, in degrees. The two always add to 90°.
Which rule to use
- Two legs known
- Pythagoras for the hypotenuse, then tan⁻¹ for the angles.
- Leg and hypotenuse
- Pythagoras rearranged for the missing leg, then sin⁻¹ or cos⁻¹.
- Side and angle
- Trigonometry. Pick sin, cos or tan depending on which sides are involved.
- Angles only
- Not enough. It fixes the shape but not the size.
- Area
- ½ × leg × leg. The two legs are the base and height already.
What this assumes
One angle is exactly 90°. Without that, the general triangle calculator is the right tool.
Angles are in degrees, which is the usual convention for geometry.
How to calculate a right triangle
Two sides means Pythagoras. A side plus an angle means picking the right trig ratio.
- c
- The hypotenuse, opposite the right angle
- opposite / adjacent
- Named relative to the angle you are using
Find the hypotenuse. It is always opposite the right angle and always the longest side.
With two sides, use Pythagoras. Square, add or subtract, then square root.
For angles, use an inverse ratio. Knowing both legs, tan⁻¹(opposite ÷ adjacent) gives the angle.
Get the last angle free. The two non-right angles add to 90°, so subtract the one you found from 90.
See a worked example: the angles in a 3-4-5 triangle
- Legs
- 3 and 4
- Hypotenuse
- 5
For the angle opposite the side of 3: tan(A) = 3 ÷ 4 = 0.75.
tan⁻¹(0.75) = 36.87°.
The other angle: 90 − 36.87 = 53.13°.
Area: ½ × 3 × 4 = 6, since the two legs already meet at a right angle and act as base and height.
36.87° and 53.13°, area 6
Frequently asked questions
Pythagoras works with sides only: give it two, it returns the third.
This one also handles angles, so you can start from a side and an angle, or find the angles from the sides. Use Pythagoras when sides are all you care about, and this when angles are involved.
A memory aid for the three ratios. Sin = Opposite/Hypotenuse, Cos = Adjacent/Hypotenuse, Tan = Opposite/Adjacent.
Pick whichever ratio uses the two sides you actually have. If you know the opposite and adjacent, that is tan.
Use the inverse function, written sin⁻¹, cos⁻¹ or tan⁻¹ and often labelled arcsin, arccos and arctan.
With legs of 3 and 4, tan⁻¹(3 ÷ 4) = 36.87°. The ordinary tan key goes from angle to ratio; the inverse goes back the other way.
It depends on the angle you are working with. Opposite is across from that angle, adjacent is the leg touching it that is not the hypotenuse.
They swap when you switch to the other angle, which is exactly where mistakes creep in. The hypotenuse is the only side that never changes role.
45-45-90 has two equal legs and a hypotenuse of leg × √2. 30-60-90 has sides in the ratio 1 : √3 : 2.
They are worth recognising because they appear constantly and can be solved instantly without a calculator.
Problems people actually run into
Working in radians when the answer should be degrees
A calculator left in radian mode gives 0.6435 instead of 36.87°. The number looks like a plausible answer to a different question, so it often survives to the final line.
Check the mode indicator before any trig work. A quick test: sin(30) should give exactly 0.5 in degrees. If it gives −0.988, you are in radians.
Treating the longest side as a leg
The hypotenuse is always the longest side and always opposite the right angle. Feeding it in as a leg produces a negative under the square root, or a nonsense answer.
If the calculator says a triangle is impossible, this is usually why. Check which side is genuinely the longest before entering anything.
Results are estimates for general information only and are not professional financial, medical, or legal advice. Read our full disclaimer.
Last updated: September 4, 2026