GEOMETRY, MADE CLEAR
Right triangle solver
Calculate missing sides, angles, area, and perimeter from two sides or a side and an angle. Explore the diagram and each step.
Your triangle
a ⟂ b · c is the hypotenuseDrawn to scaleClick a known side label to edit
All measurements
- Leg a
- 3m
- Leg b
- 4m
- Hypotenuse c
- 5m
- Angle A
- 36.87°
- Angle B
- 53.13°
- Area
- 6m²
How we got there
Find the hypotenuse
c = √(3² + 4²) = √25 = 5 m
The Pythagorean theorem relates the two perpendicular legs and the hypotenuse.
Find the acute angles
A = arctan(3 / 4) ≈ 36.87°; B = 90° − A ≈ 53.13°
Calculate area and perimeter
Area = (3 × 4) / 2 = 6 m²; Perimeter = 3 + 4 + 5 = 12 m
Trigonometric ratios & radians
- sin(A) = a/c
- cos(A) = b/c
- tan(A) = a/b
RIGHT TRIANGLE FORMULAS
How to solve a right triangle
A right triangle has one 90° angle. Its perpendicular legs are a and b, and the hypotenuse c is the longest side. Angle A faces a, and angle B faces b. Supply two independent measurements: two sides, or one side and one acute angle. The calculator then finds the remaining measurements.
Choose the formula for your known measurements
| Find | Known measurements | Formula |
|---|---|---|
| Hypotenuse c | Legs a and b | c = √(a² + b²) |
| Leg a | c and b | a = √(c² − b²) |
| Leg b | c and a | b = √(c² − a²) |
| Both legs | c and A | a = c sin(A); b = c cos(A) |
| Hypotenuse c | a and A / b and A | c = a / sin(A); c = b / cos(A) |
| Angle A | a and b | A = arctan(a / b) |
| Angle B | Angle A | B = 90° − A |
| Area | a and b | Area = ab / 2 |
| Perimeter | a, b, and c | P = a + b + c |
Worked example: a 3–4–5 triangle
For a = 3 m and b = 4 m, c = √(9 + 16) = 5 m. The acute angles are approximately 36.87° and 53.13°. Area is 6 m², perimeter is 12 m, and the perpendicular altitude to the hypotenuse is ab / c = 2.4 m.
Check your answer
Both legs must be positive, the hypotenuse must be longer than each leg, and the acute angles must add to 90°. Convert lengths to the same unit before applying a formula. Degrees and radians describe the same angles with different numbers; choose the matching angle mode.
Read how to find a missing side, find a missing angle, or use SOH CAH TOA.
UNDERSTAND THE METHOD
A little geometry goes a long way.
How to find the hypotenuse
Find the hypotenuse of a right triangle from two legs or one side and an angle. Learn the formulas with step-by-step examples.
4 min readGUIDE 02How to find a missing right triangle angle
Find a missing right triangle angle with inverse sine, cosine, or tangent. Includes a 3–4–5 example and degree-to-radian explanation.
4 min readGUIDE 03SOH CAH TOA, explained visually
Learn SOH CAH TOA: sine, cosine, and tangent with opposite, adjacent, and hypotenuse labels, rearranged formulas, and a worked example.
5 min readGUIDE 0430–60–90 and 45–45–90 triangles
Use 30–60–90 and 45–45–90 triangle formulas and exact side ratios. Compare worked examples, radicals, and Pythagorean triples.
4 min readGUIDE 05Right triangles in practical measurements
Calculate rectangle diagonals, rise-and-run slope angles, and sloping lengths with right triangle formulas, consistent units, and worked examples.
5 min readGUIDE 06How to find a missing side of a right triangle
Find a missing leg or hypotenuse using Pythagoras or an acute angle. Includes worked examples, formulas, and common mistakes.
4 min readQUICK ANSWERS
Frequently asked questions.
A few useful details about inputs, angles, and accuracy.
More questionsWhat information do I need to solve a right triangle?
Two independent measurements in addition to the known 90° angle. Enter two side lengths, or one side length and one acute angle. Two angles alone determine shape, but not size.
Which side is the hypotenuse?
Side c is the hypotenuse: the longest side, opposite the 90° angle. In our diagram, a is the vertical leg, b is the horizontal leg, and angle A is opposite a.
Can I enter feet and inches or fractions?
Yes. Enter 5 ft 6 in for a combined length, or a fraction such as 3/4. You can also enter a unit suffix such as 150 cm. A suffix overrides the default input unit; results are converted to your selected output unit.
How do degrees and radians work?
Use the angle input selector for degrees or radians. Radians accept decimal values and expressions such as pi/6. The main results display degrees, with radians included under trigonometric ratios.
Why do I get an error for my measurements?
Lengths must be positive. A known hypotenuse must be longer than the known leg, and an acute angle must be greater than 0° and less than 90°. Very extreme triangles may exceed reliable numerical precision.
Are results and explanations calculated with AI?
No. Results use the Pythagorean theorem and trigonometric formulas directly in your browser. Worked solutions come from those same calculations. Inputs are not sent to a calculation server.
Can I use this for a triangle without a right angle?
No. This calculator assumes exactly one 90° angle. For a general triangle, you need other methods such as the Law of Sines or Law of Cosines.
Can I print or share the solution?
Yes. Print / PDF opens your browser’s print dialog, where you can choose Save as PDF. Copy link creates a URL that reopens the exact inputs, and Download diagram saves an SVG image.
Formulas you can inspect.
Every answer comes from Pythagoras and trigonometry. No AI guesses, no sign-up, and no calculation uploads. Our approach