Triangle Calculator · Practical guide
How to Find the Area of a Triangle With 3 Sides
No height needed — Heron's formula turns any three side lengths into the area. The SSS tab above does it automatically.
At a glance
Use Heron's Formula
When you know all three sides, compute the semi-perimeter s = (a + b + c) ÷ 2, then Area = √(s(s − a)(s − b)(s − c)). For the classic 3-4-5 triangle: s = 6 and Area = √(6 × 3 × 2 × 1) = √36 = 6 square units. Enter any three sides in the SSS tab above and the calculator returns the area along with every angle.
Interactive tool
Triangle Calculator
Enter your own values, then compare the result with the examples below.
Triangle Solution
Worked Example Step by Step
- Sides a = 3, b = 4, c = 5
- Semi-perimeter: s = (3 + 4 + 5) ÷ 2 = 6
- Subtract each side: 6 − 3 = 3, 6 − 4 = 2, 6 − 5 = 1
- Multiply and root: √(6 × 3 × 2 × 1) = √36 = 6
Areas of Common Triangles
| Sides | Semi-Perimeter | Area |
|---|---|---|
| 3, 4, 5 | 6 | 6.00 |
| 5, 5, 6 | 8 | 12.00 |
| 6, 8, 10 | 12 | 24.00 |
| 7, 8, 9 | 12 | 26.83 |
Check the Triangle Exists First
Not every three lengths form a triangle: the sum of any two sides must exceed the third. Sides of 2, 3, and 6 fail because 2 + 3 = 5 is less than 6 — the two short sides can't meet. The calculator alerts you when this triangle inequality rule is violated.
Frequently Asked Questions
Can I use base times height instead?
Yes, if you know the height: Area = 1/2 × base × height. Heron's formula is the practical choice when only the three side lengths are known.
What units is the area in?
Square units of whatever unit the sides use. Sides measured in feet give an area in square feet; sides in meters give square meters.
Does Heron's formula work for all triangles?
Yes — acute, right, and obtuse triangles alike, as long as the three sides satisfy the triangle inequality.
What happens if the sides can't form a triangle?
The formula produces no real answer — the expression under the square root goes negative. The calculator catches this and shows an alert instead.