Right Triangle Calculator
A right triangle is fixed entirely by its two legs: the Pythagorean theorem gives the hypotenuse, half their product gives the area, and the arctangent of their ratio gives the acute angles. Enter leg a and leg b to see all of it, along with the arithmetic behind each figure.
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Hypotenuse c
5.000000 units
Perimeter
12.000000 units
Details
Updates as you typeOne of the two sides that meet at the right angle. Must be greater than zero.
The other side touching the right angle. Use the same unit for both legs.
Summary
Hypotenuse
5.000000 units
- Area
- 6.000000
- Perimeter
- 12.000000 units
- Angle A (opposite leg a)
- 36.8699 °
- Angle B (opposite leg b)
- 53.1301 °
- Altitude to the hypotenuse
- 2.400000 units
- Inradius
- 1.000000 units
- Both legs must meet at the right angle. If you know the hypotenuse and one leg instead, the missing leg is √(c² − a²).
- The angles are reported in degrees and always sum to 90°, because the third angle already uses the other 90° of the triangle.
- The circumcentre of a right triangle sits at the midpoint of the hypotenuse, which is why the circumradius is exactly half of c.
How this is calculated
- Leg a
- 3.000000 units
- Leg b
- 4.000000 units
- a² + b²
- 25.000000
- c = √(a² + b²)
- 5.000000 units
- Area = a × b ÷ 2
- 6.000000
- Perimeter = a + b + c
- 12.000000 units
- A = atan(a ÷ b)
- 36.8699 °
- B = 90° − A
- 53.1301 °
- Circumradius = c ÷ 2
- 2.500000 units
Compare scenarios
See how one change moves the result
- CurrentYour inputs as they stand5.000000 unitsCurrent
- Leg aunits 3.85.517246 units
- Leg bunits 55.830952 units
Frequently asked questions
How do I find the hypotenuse from the two legs?
Square each leg, add the squares, and take the square root: c = √(a² + b²). With legs of 3 and 4 that is √(9 + 16) = √25 = 5, the classic 3-4-5 triangle used by builders to check a square corner.
How are the acute angles calculated?
The angle opposite leg a satisfies tan(A) = a ÷ b, so A = atan(a ÷ b) converted from radians to degrees. The other acute angle is simply 90° − A, because the three angles of any triangle add to 180° and one of them is already the right angle.
Why is the area just a × b ÷ 2?
The two legs meet at 90°, so they act as the base and the height directly with no extra trigonometry needed. Two identical right triangles glued along the hypotenuse form a rectangle of area a × b, and each triangle is half of it.
What if I know the hypotenuse and only one leg?
Rearrange the same theorem: the missing leg is √(c² − a²). Work that out first, then enter the two legs here to get the area, the perimeter and both angles. The hypotenuse must be longer than the leg, or no such triangle exists.
Do the legs have to be in any particular unit?
No, but both legs must use the same unit. The hypotenuse and perimeter then come back in that unit, the area in that unit squared, and the angles in degrees regardless of the length unit you chose.