Triangle Calculator
Triangle area from base and height, or area and perimeter from three sides (Heron).
Quick answer
- Formula: Base–height: Area = (b × h) ÷ 2 · Heron: Area = √(s(s−a)(s−b)(s−c)), where s = (a+b+c) ÷ 2
- Worked example — Area: 6.0000 (full example below).
Triangle Calculator
| Area | 6.0000 |
| Perimeter (three-sides mode) | 12.0000 |
| Semi-perimeter (three-sides mode) | 6.0000 |
The 3-4-5 triangle: perimeter 12, semi-perimeter 6, and Heron's formula gives √(6 × 3 × 2 × 1) = √36 = 6 for the area — matching (3 × 4) ÷ 2 from the base–height method.
There are two common ways to size a triangle. If you know the base and the vertical height, the area is half their product. If you know all three sides instead, Heron's formula finds the area from the sides alone — no height needed.
Choose the mode that matches what you know. In three-sides mode the calculator also returns the perimeter and semi-perimeter, and it checks the triangle inequality: the two shorter sides must together exceed the longest side, or no such triangle exists.
The formula
Worked example
The 3-4-5 triangle: perimeter 12, semi-perimeter 6, and Heron's formula gives √(6 × 3 × 2 × 1) = √36 = 6 for the area — matching (3 × 4) ÷ 2 from the base–height method.
The example is pre-loaded in the result panel — press Calculate with your own numbers to replace it.
Frequently asked questions
Why can't I get a perimeter from base and height?
Because many different triangles share the same base and height but have differently slanted sides — sliding the apex sideways keeps the area identical while stretching the perimeter. Perimeter is only shown in three-sides mode.
What is the triangle inequality?
Any two sides of a triangle must add up to more than the third side. Sides of 2, 3 and 6 cannot form a triangle because 2 + 3 < 6 — the two short sides cannot reach each other, and the calculator flags this.
Category: Math calculators
Sources & methodology
This calculator applies the formula shown on this page exactly as written, using the standard definitions for its inputs. Results are computed from the values you enter — no data is stored — and are rounded only for display.
Content last reviewed by CalcHub Editorial.
Embed this calculator on your site
Free to use with attribution — paste the snippet below and the calculator appears on your page, with a link back to CalcHub.
Related calculators
Area Calculator
Area of a square, rectangle, circle, triangle, trapezoid, parallelogram or ellipse.
Pythagorean Theorem Calculator
Find the hypotenuse or a missing leg of a right triangle.
Perimeter Calculator
Perimeter of squares, rectangles, triangles and regular polygons, plus circumference.
Circle Calculator
Diameter, circumference and area from a circle's radius.