EVERYDAY MATH
Right triangle calculator
Solve a right triangle from two sides or one side and an acute angle, with all sides, acute angles, area and perimeter calculated from one shared model.
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No regional currency, unit or language profile is applied. This choice does not convert values or change formulas, results, routes or legal guidance.
Choose a sufficient measurement pair. Sides a and b meet at the right angle; c is the hypotenuse. Angle A is opposite side a.
Solved right triangle
Hypotenuse c: 5- Leg a
- 3
- Leg b
- 4
- Angle A
- 36.86989765°
- Angle B
- 53.13010235°
- Area
- 6 square units
- Perimeter
- 12 units
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Verification and calculation details
- Purpose
- Right triangle calculator
- Variables and units
- Use the labelled fields and units shown in the calculator. Results use those units unless a conversion is stated.
- Formula and method
- The exact formula and worked example are shown below. Deterministic formula executed locally in the browser.
- Assumptions
- Only entered values and stated assumptions are included. Local fees, rules and professional requirements are excluded unless explicitly shown.
- Engine version
- 1.0.0
- Production verification baseline
- Release 63 · source
998803f - Verification run
release-v63-2026-09-20- Last verified
- — Automated release checks passing
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How this calculator works
For perpendicular legs a and b and hypotenuse c, a²+b²=c². With two sides, solve the missing side from that relationship. With acute angle A opposite side a, use sin(A)=a/c, cos(A)=b/c and tan(A)=a/b. The second acute angle is B=90°−A. Area=ab/2 and perimeter=a+b+c.
Variables and inputs
- Known measurements
- Required numeric input. allowlisted measurement-pair selection; two sides or one side plus angle A.
- First known measurement
- Required numeric input. finite; greater than zero; side lengths no more than 1 trillion units.
- Second known measurement
- Required numeric input. finite; greater than zero; angle A must be less than 90 degrees when selected.
- Known side for side-angle mode
- Optional numeric input. allowlisted side a, b or c.
How to interpret the result
The calculator returns legs a and b, hypotenuse c, acute angles A and B, area, perimeter. Read each output against the assumptions you entered, compare alternatives one variable at a time, and use the result as an estimate rather than a promise.
Common mistakes to avoid
- Mixing units or entering a rate as a decimal when the field requests a percentage.
- Rounding intermediate values instead of the final displayed result.
- Leaving out a cost, timing rule or local requirement listed in the assumptions below.
Practical uses
Use the right triangle calculator to check a real scenario, compare a changed assumption and explain the arithmetic before relying on a quote, specification or decision.
Worked example
For legs a=3 and b=4, c=√(3²+4²)=5. Angle A=atan2(3,4)≈36.8699°, angle B≈53.1301°, area=3×4/2=6 square units and perimeter=3+4+5=12 units.
Assumptions and limitations
- the triangle contains one exact 90-degree angle
- a and b are the perpendicular legs and c is the hypotenuse
- angle A is opposite side a and angle B is opposite side b
- all supplied side lengths use the same unit
- does not solve oblique triangles
- measurements do not account for survey, manufacturing or construction tolerance
- near-degenerate inputs may be sensitive to measurement error
- displayed decimals are rounded after full-precision calculation
Important notes
Results are estimates based on the values entered. Confirm rates, prices, units and professional requirements that apply in your location. Review the Answer Atlas Calculation Standard and corrections policy for formula, privacy and correction rules.
Frequently asked questions
What measurements are enough to solve a right triangle?
Enter any two sides, or one side and acute angle A. A side is required because angles alone determine shape but not size.
Which side is the hypotenuse?
Side c is opposite the 90-degree angle and must be longer than either leg a or b.
Can this solve a triangle without a right angle?
No. The formulas and validation apply only to right triangles. A non-right triangle requires different information and formulas.