Triangle Calculator
Solve any triangle from three known values using the sine and cosine rules.
About Triangle Calculator
For a right triangle, the Pythagorean theorem gives the hypotenuse c = √(a² + b²). The area is half the product of the two legs, and the two non-right angles are found with the arctangent of the leg ratio.
Formulas
Hypotenuse — Pythagorean theorem
c = √(a² + b²)
- a
- First leg (perpendicular side)
- b
- Second leg (perpendicular side)
- c
- Hypotenuse (side opposite the right angle)
Angles — Law of Sines (right triangle)
a / sin(A) = b / sin(B) = c / sin(90°) = c → A = arctan(a / b), B = 90° − A
- A
- Angle opposite leg a
- B
- Angle opposite leg b
- C
- Right angle (90°)
Area
Area = (a × b) ÷ 2
Perimeter
Perimeter = a + b + c
Worked example
With the default values below, Triangle Calculator returns Hypotenuse (c) of 5.0000. Change any input above and every figure here is recalculated in your browser.
Inputs used
- Leg aaccepts 0–1,000,000 units
- 3 units
- Leg baccepts 0–1,000,000 units
- 4 units
Results
- Hypotenuse (c)
- 5.0000
- Area
- 6.0000
- Perimeter
- 12.0000
- Angle opposite a (°)
- 36.87
- Angle opposite b (°)
- 53.13
Step by step
- 1Apply the Pythagorean theorem to find the hypotenuse= 5.0000
- 2Find angle A using the Law of Sines: sin(A) = a / c= 36.87°For a right triangle sin(A) = a/c = tan(A)·cos(A); arctan(a/b) is equivalent and numerically stable.
- 3Angle B = 90° − A (angles in a triangle sum to 180°)= 53.13°
- 4Calculate the area= 6.0000
- 5Calculate the perimeter= 12.0000
Assumptions and limits
- The result is derived only from the 2 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 4 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
Does this work for non-right triangles?
This calculator assumes a right triangle (one 90° angle) defined by its two perpendicular legs. Other triangles need side-angle-side or law-of-cosines methods.
What units does it use?
It's unit-agnostic — enter both legs in the same unit and all outputs use that unit (area is in that unit squared).