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- Solves a right triangle from any two values: two sides, or one side and an angle.
- Gives all three sides and both acute angles in degrees and radians.
- Also shows area, perimeter, height to the hypotenuse, inradius and circumradius.
- Checks the answer with a² + b² = c².
How to use the right triangle calculator
Pick what you know
Two legs, a leg and the hypotenuse, or one side and angle A.
Enter the values
Side a is opposite angle A, side b is next to it, and c is the hypotenuse.
Read the solved triangle
All sides and angles appear at once.
Use the extras
Area, perimeter, altitude and the radius of the inscribed and circumscribed circles are included.
How a right triangle is solved
From two sides
c = √(a² + b²)
A = arctan(a ÷ b), B = 90° − A
When the hypotenuse is known, a = √(c² − b²) and A = arcsin(a ÷ c).
From a side and an angle (SOH CAH TOA)
sin A = a ÷ c
cos A = b ÷ c
tan A = a ÷ b
Rearrange whichever ratio contains the side you know and the side you need.
Other measurements
Area = a × b ÷ 2
Height to hypotenuse = a × b ÷ c
Inradius = (a + b − c) ÷ 2, Circumradius = c ÷ 2
Example 1: legs 3 and 4
The classic 3-4-5 triangle.
- Hypotenuse 5
- Angles 36.8699° and 53.1301°
- Area 6
- Perimeter 12
- Inradius 1
Any multiple, such as 6-8-10, has the same angles.
Example 2: hypotenuse and an angle
c = 10, A = 30°.
- a = c × sin A 5
- b = c × cos A 8.6603
- B 60°
In a 30-60-90 triangle the short leg is always half the hypotenuse.
Example 3: a leg and an angle
b = 10, A = 60°.
- a = b × tan A 17.3205
- c = b ÷ cos A 20
- B 30°
This is the same 30-60-90 shape, scaled up.
Where a right triangle calculator helps
Geometry and trig homework
Solve every side and angle and check your SOH CAH TOA working.
Roofs and ramps
Find rafter length and pitch angle from rise and run.
Ladders and stairs
Work out the safe angle and reach of a ladder against a wall.
Surveying and navigation
Find distances and bearings across land or on a map.
If you only need the missing side, the Pythagorean theorem calculator is quicker. Get sin, cos and tan of any angle with the trig calculator, or measure roof steepness with the roof pitch calculator.
Right triangle calculator FAQ
How do you solve a right triangle?
You need two values besides the right angle, and at least one must be a side. Use the Pythagorean theorem for sides and sin, cos or tan for angles.
What is SOH CAH TOA?
A memory aid: Sine = Opposite ÷ Hypotenuse, Cosine = Adjacent ÷ Hypotenuse, Tangent = Opposite ÷ Adjacent.
Can I solve a right triangle from two angles?
No. Two angles fix the shape but not the size. You need at least one side length.
Which side is a and which is b?
Side a is opposite angle A. Side b is the other leg, next to angle A. Side c is the hypotenuse.
How do I find the area of a right triangle?
Multiply the two legs and divide by 2. For legs 3 and 4 the area is 6.
Why does it say the hypotenuse must be longer?
The hypotenuse is always the longest side of a right triangle. A shorter value means the numbers cannot form a right triangle.