Right Triangle Calculator
Solve all sides, acute angles, area, perimeter and inradius of a right triangle from two known sides or a side and angle.
- Five common known-value modes
- Solves all sides and both acute angles
- Reports area, perimeter and inradius
Calculator workspace
Enter the known values, calculate, and review the supporting figures and formula instead of relying on a single unexplained number.
What this Right Triangle Calculator does
A right triangle is completely determined by two independent measurements as long as at least one is a side. This calculator goes beyond a simple Pythagorean diagonal: you can start from two legs, a hypotenuse and leg, a hypotenuse and acute angle, an adjacent leg and angle, or an opposite leg and angle. It then solves the full triangle using consistent side labels and trigonometric identities.
The workspace is designed for quick checking as well as repeatable planning. Inputs remain editable, the supporting figures are shown with the headline result, and the calculation runs locally in the browser. That makes it easy to change one assumption at a time, compare scenarios and copy or save a result together with the values that explain it.
Formula and calculation method
sin(A)=a/c, cos(A)=b/c, tan(A)=a/b and a²+b²=c².
The calculator defines side a opposite acute angle A, side b adjacent to angle A, and c as the hypotenuse. Depending on the selected mode it combines the Pythagorean theorem with sine, cosine or tangent. After solving a, b and c, it calculates the complementary acute angle B = 90° − A, the area a×b÷2, perimeter a+b+c and inradius (a+b−c)÷2. This gives a compact geometric profile useful for layout, fabrication, classroom checks and design sketches.
How to use the calculator
- Choose the calculation mode, shape, unit or known-value combination when the page provides one.
- Enter values that belong to the same problem or measurement scenario and keep units consistent with the field labels.
- Select Calculate and review both the main answer and the supporting metrics shown with it.
- Change one assumption at a time when comparing scenarios; this makes the effect of each input easier to understand.
- Use Copy Result, Share Result or Save Result Image when you need a portable record of the calculation.
Worked example
If the known legs are a = 3 and b = 4, the calculator finds c = 5. Angle A is arctan(3/4) ≈ 36.87°, angle B ≈ 53.13°, area = 6 square units, perimeter = 12 units and inradius = 1 unit. If instead you know c = 5 and A = 36.87°, the trigonometric mode returns essentially the same triangle.
How to interpret the result
The angle modes expect degrees and require an acute angle strictly between 0° and 90°. When entering a hypotenuse and a leg, the hypotenuse must be longer than the leg. For physical measurements, use the same length unit for the two known sides; every solved side will then use that same unit, area will use the squared unit and the angles remain in degrees.
A calculator result is only as useful as the values entered. For measurements, use appropriately precise source data; for costs, use prices that match the same currency and period; for technical work, compare the output with drawings, equipment data or other authoritative information. The supporting metrics on this page are included specifically to make cross-checking easier.
Important assumptions and limitations
This is not a general oblique-triangle calculator. It assumes one angle is exactly 90°. Real construction measurements can deviate from a mathematical right angle, so a calculated diagonal should be checked against actual site conditions, material tolerances and instrument precision before cutting or installation.
This calculator is provided for planning, checking, education and general informational use. It makes the formula and assumptions visible, but it does not replace project specifications, professional engineering, financial or medical advice, contractual documents, equipment ratings or applicable standards.
Frequently asked questions
What two values are enough to solve a right triangle?
Any two sides, or one side plus one acute angle, are sufficient when the 90-degree angle is already known.
What is the difference from the Pythagorean calculator?
The Pythagorean calculator focuses on side lengths. This tool also accepts side-and-angle combinations and reports a fuller set of triangle properties.
Can angle A be 90 degrees?
No. A is one of the two acute angles; the right angle is already fixed at 90 degrees.