Right Triangle Calculator
Solve a right triangle from any two values, with angles, area and perimeter.
About Right Triangle Calculator
A right triangle has one 90° angle. Given any two sides (or a side and an acute angle), all remaining values follow from the Pythagorean theorem (a² + b² = c²) and the six trigonometric functions. Angles A and B are always complementary: A + B = 90°. The area is simply half the product of the two legs.
Formulas
Pythagorean theorem
c = √(a² + b²)
- a
- Leg a (shorter side)
- b
- Leg b
- c
- Hypotenuse
Angles from sides
A = arctan(a/b), B = 90° − A
Area
Area = a × b / 2
Worked example
With the default values below, Right Triangle Calculator returns Hypotenuse c of 5.000000. Change any input above and every figure here is recalculated in your browser.
Inputs used
- Known valuesone of Leg a and Leg b, Leg a and Hypotenuse c, Leg b and Hypotenuse c, Leg a and Angle A, Leg b and Angle B
- Leg a and Leg b
- Leg aminimum 0
- 3
- Leg bminimum 0
- 4
- Hypotenuse cminimum 0
- 5
- Angle A (degrees, opposite to leg a)accepts 0–90
- 36.87
- Angle B (degrees, opposite to leg b)accepts 0–90
- 53.13
Results
- Hypotenuse c
- 5.000000
- Leg a
- 3.000000
- Leg b
- 4.000000
- Angle A
- 36.8699 °
- Angle B
- 53.1301 °
- Area
- 6.000000
- Perimeter
- 12.000000
Step by step
- 1Apply Pythagorean theorem= c = √(9 + 16) = 5
- 2Angle A (opposite a)= 36.869898°
- 3Angle B (opposite b)= 53.130102°
- 4Area= 6
- 5Perimeter= 12
Assumptions and limits
- The result is derived only from the 6 inputs listed above. Anything not among them is not part of the calculation.
- In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
- Figures are rounded for display to 6 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.
How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.
Frequently Asked Questions
What is the Pythagorean theorem?
It states that for any right triangle, the square of the hypotenuse equals the sum of the squares of the other two sides: a² + b² = c². The classic example is the 3-4-5 triangle: 3² + 4² = 9 + 16 = 25 = 5².
How do you find a missing side when you have a side and an angle?
Use trigonometry. If you know leg a and angle A (opposite to a), then b = a / tan(A) and c = a / sin(A). If you know the hypotenuse and an angle, the legs are c·sin(A) and c·cos(A).
Why do right triangle angles always add to 180°?
The right angle is exactly 90°, and the remaining two angles A and B must together fill the other 90°, so A + B + 90° = 180°. This is true for every triangle — the sum of interior angles is always 180°.
What is the difference between legs and the hypotenuse?
The two shorter sides that form the right angle are called legs (a and b). The side opposite the right angle — always the longest side — is the hypotenuse (c).