Triangle Size Calculator
Type the lengths of the three sides in any unit. The calculator checks that they form a triangle, then gives the area, perimeter, all three angles, the height and the triangle type.
- Heron's formula
- All three angles
- Type and height
Use the same unit for all three sides. The area is in that unit squared.
Three sides fix a triangle completely. Unlike four-sided shapes, a triangle cannot flex once its sides are set. That is why roof trusses and bridges are built from triangles, and why three measurements are enough to find every angle and the exact area.
Well-known triangles
Useful triangles with whole number sides. Search by side length or type.
| Sides | Type | Angles | Area | Perimeter |
|---|---|---|---|---|
| 3, 4, 5 | Right, scalene | 36.9°, 53.1°, 90° | 6 | 12 |
| 5, 12, 13 | Right, scalene | 22.6°, 67.4°, 90° | 30 | 30 |
| 8, 15, 17 | Right, scalene | 28.1°, 61.9°, 90° | 60 | 40 |
| 1, 1, 1 | Equilateral | 60°, 60°, 60° | 0.433 | 3 |
| 5, 5, 6 | Isosceles, acute | 53.1°, 53.1°, 73.7° | 12 | 16 |
| 5, 5, 8 | Isosceles, obtuse | 36.9°, 36.9°, 106.3° | 12 | 18 |
| 5, 6, 7 | Scalene, acute | 44.4°, 57.1°, 78.5° | 14.7 | 18 |
| 4, 6, 9 | Scalene, obtuse | 20.7°, 32.1°, 127.2° | 9.56 | 19 |
Builders use the 3-4-5 triangle to set out square corners. Measure 3 along one wall, 4 along the other, and adjust until the diagonal is exactly 5.
The angle between two sides
Two sides of 5 units each. Slide the angle between them.
Area is half of side × side × sine of the angle between them. It is largest when the sides meet at a right angle and falls to zero as they fold flat.
How to solve a triangle from three sides
The method the calculator uses. Step through it with the 5, 6, 7 example.
Check it is a triangle
5 + 6 > 7, so these sides work.
The triangle inequality comes first. If the two shorter sides add up to the longest side or less, they lie flat and there is no triangle.
Types of triangle
Named by sides and by angles. Pick a type.
All sides equal and every angle 60°.
Two equal sides with equal angles opposite them.
No sides equal and no angles equal.
One angle of exactly 90°. The sides follow a² + b² = c².
Every triangle has one name from each list, such as an isosceles right triangle or a scalene obtuse triangle.
Measuring a real triangle
For gardens, roofs and plots. Tick each step.
Tick each item as you go.
On land, measure each side twice. A small error on a long side changes the angles much less than the same error on a short side.
What the result tells you
Everything about your triangle. Each tile explains one result.
Using Heron's formula.
The three sides added.
All three in degrees.
Named by sides and by angles.
The perpendicular onto side c.
The height onto side c is useful for working out roof rise, ramp height and material cuts, where you need the perpendicular distance.
Frequently Asked Questions
No question matches that search.
How do I find the area of a triangle with three sides?
Use Heron's formula: find s = half the perimeter, then area = √(s(s − a)(s − b)(s − c)).
How do I find the angles from three sides?
Use the law of cosines. cos A = (b² + c² − a²) ÷ (2bc), then take the inverse cosine.
Can any three lengths make a triangle?
No. Each pair of sides must add up to more than the third side.
How do I know if a triangle is right-angled?
If the squares of the two shorter sides add up to the square of the longest side, it has a 90° angle.
What is the area of a 3-4-5 triangle?
6 square units. It is a right triangle, so area is ½ × 3 × 4.
What units does the area use?
The square of whatever unit you entered. Sides in metres give square metres.
Do the angles always add to 180°?
Yes, in any flat triangle.
Three numbers, the whole triangle
Measure the three sides in one unit, check they pass the triangle test and the calculator gives you the area, perimeter, angles, height and type. It works for homework, roofs, gardens and plots alike.
More size calculators
Each one has its own calculator, worked examples and answers to common questions.