Calculator Form
Choose a solving method, enter the known values, and the page will compute the missing parts of the right triangle.
Example Data Table
| Case | Known Inputs | Main Outputs |
|---|---|---|
| Two legs | a = 3, b = 4 | c = 5, Area = 6, Angle A ≈ 36.87° |
| Leg and hypotenuse | a = 5, c = 13 | b = 12, Area = 30, Angle A ≈ 22.62° |
| Hypotenuse and angle | c = 20, Angle A = 30° | a = 10, b ≈ 17.3205, Area ≈ 86.6025 |
| Area and leg | Area = 24, a = 6 | b = 8, c = 10, Perimeter = 24 |
Formula Used
- Pythagorean theorem: c² = a² + b²
- Area: Area = (a × b) / 2
- Perimeter: Perimeter = a + b + c
- Angle A: tan(A) = a / b, sin(A) = a / c, cos(A) = b / c
- Angle B: B = 90° − A
- Altitude to hypotenuse: h = (a × b) / c
- Inradius: r = (a + b − c) / 2
- Circumradius: R = c / 2
- Median to hypotenuse: m = c / 2
How to Use This Calculator
- Select the solving mode that matches your known values.
- Enter the available side, angle, or area measurements.
- Add a unit label such as cm, m, or ft.
- Choose the number of decimal places you want.
- Press Calculate Right Triangle to generate the result.
- Review the table, graph, and geometric measures above the form.
- Download the result as CSV or PDF when needed.
FAQs
1) What does this right angle calculator solve?
It solves missing sides, acute angles, area, perimeter, altitude to the hypotenuse, inradius, circumradius, and related trigonometric values for a right triangle.
2) Which inputs are enough for a right triangle?
You need any valid pair that uniquely determines the triangle, such as two legs, one leg with the hypotenuse, one side with one acute angle, or area with one leg.
3) Why must the angle be less than 90 degrees?
A right triangle already contains one 90° angle. The remaining two angles must be acute, so each must stay greater than 0° and less than 90°.
4) Why must the hypotenuse be the largest side?
The hypotenuse lies opposite the right angle, making it always longer than either leg. If it is not largest, the triangle cannot be right angled.
5) Can I use any measurement unit?
Yes. Enter a simple unit label like mm, cm, m, in, or ft. The calculator keeps the same unit consistently across side, perimeter, and radius outputs.
6) What does the altitude to the hypotenuse mean?
It is the perpendicular segment from the right angle vertex to the hypotenuse. This value is useful in geometry proofs, area relations, and triangle decomposition problems.
7) What is the difference between inradius and circumradius?
The inradius belongs to the inscribed circle touching all three sides. The circumradius belongs to the circle passing through all three vertices of the triangle.
8) Why is there a graph on the page?
The graph helps you visualize the solved triangle shape. It confirms the leg lengths and gives a quick geometric check before using or exporting the result.