Three measured edges
For a = 3, b = 4, and c = 5, the area is 6 square units, perimeter is 12 units, and C is 90°. The altitude to c is 2.4 units.
Triangle Calculator inputs
Changing the unit relabels the numbers. Convert measurements to one common unit before entering them.
SSS, SAS, and two angles with side c are supported. Angles use degrees. SSA is not supported; do not place an opposite angle into the included-angle field.
Calculated measurements
Area
6 units²
| Measurement | Value |
|---|---|
| Area | 6 units² |
| Perimeter | 12 units |
| Side a | 3 units |
| Side b | 4 units |
| Side c | 5 units |
| Angle A | 36.8698976° |
| Angle B | 53.1301024° |
| Angle C | 90.0000000° |
| Altitude to side c | 2.4 units |
| Inradius | 1 units |
| Circumradius | 2.5 units |
Formula: s = (a + b + c)/2; area = √[s(s − a)(s − b)(s − c)]
Side a is opposite angle A, and likewise for b/B and c/C. SSA is not supported; the selected modes determine one triangle.
Results use full floating-point precision internally and display up to 10 significant digits. Angles are in degrees.
Calculations run locally in your browser. Measurement values are not sent to a calculation service. The downloadable text contains your selected inputs and computed results.
How to use the Triangle Calculator
- 01
Choose the measurements you actually know: SSS, SAS, or angles A/B with side c.
- 02
Match lowercase sides to the opposite uppercase angles. In SAS mode, angle C lies between sides a and b.
- 03
Enter lengths in one unit and angles in degrees. Read validation before relying on a result.
- 04
Inspect the diagram and download or copy the measurements with their formulas.
Examples
An included right angle
For a = 6, b = 8, and C = 90°, side c is 10, area is 24, and the perimeter is 24. C must be the angle between the entered sides.
Two angles fix the shape
With A = 60°, B = 60°, and c = 7, the remaining angle is 60° and every side is 7. The area is approximately 21.21762239 square units.
Choose a solvable input set
Three sides fix the triangle up to reflection when the triangle inequality holds. Two sides plus their included angle also fix it. Two angles determine shape but need a side to establish scale. This interface uses side c for the two-angle mode; relabel a drawing consistently when your known side has another letter.
How the formulas connect
The cosine law recovers the third side in SAS mode. For two angles, C = 180° − A − B and the sine law supplies the missing lengths. From the three sides, Heron’s formula gives area. The altitude to c follows from 2 × area/c, while the inradius is 2 × area/perimeter.
What the two circle radii mean
The incircle touches all three sides and has radius area divided by semiperimeter. The circumcircle passes through the three vertices and has radius abc/(4 × area). These values can differ greatly for a long, narrow triangle. They do not describe an arbitrary circle drawn inside or around the diagram.
Precision near a flat triangle
Sides such as 2, 3, and 5 lie on a straight line and are rejected. The solver also rejects configurations where the normalized triangle-inequality margin is at most 10⁻¹². This protects against unstable answers near degeneracy; it is a computational threshold rather than a measurement tolerance.
What to know
- SSA, angle-only input, spherical triangles, and uncertainty propagation are not supported.
- Lengths must be within 10⁻⁹–10⁹ units. Extremely degenerate configurations are rejected.
Common questions
Can I enter an SSA triangle?
No. Two sides and a non-included angle can describe zero, one, or two triangles. This tool avoids silently choosing one SSA solution. Use SSS, SAS, or two angles and side c.
Are the angles degrees or radians?
The input and reported angles are degrees. Convert radians before entering an angle. Every valid result has angles totaling approximately 180°.
Why is my triangle rejected?
Check blank fields, positive length bounds, the triangle inequality, and the angle sum. Extremely flat triangles are rejected for numerical stability even when rounded measurements look plausible.
Does the picture determine the answer?
No. The calculation uses the entered numbers. The diagram is fitted into the available space and may compress a very thin triangle visually.