Area of Triangle Calculator
Get the area of a triangle from its base and height with A = ½ × b × h, or from all three sides with Heron’s formula — no height needed.
Example: with What do you know? Base and height · Base b 10 · Height h (perpendicular to base) 6 · Side a (Heron mode) 3 · Side b (Heron mode) 4 · Side c (Heron mode) 5 → Area: 30.00.
Computed by the calculator below using its default values. Change any input to see your own numbers.
📐 Geometry practice made simple
Check it outTwo ways to find the area of a triangle
The classic area of a triangle formula is A = ½ × base × height — half of the rectangle the triangle would fill. A base of 10 with a height of 6 gives ½ × 10 × 6 = 30 square units. The height must meet the base at 90°; in an obtuse triangle that perpendicular can even land outside the shape, and the formula still holds.
No height handy? Heron’s formula needs only the three sides: compute the semiperimeter s = (a + b + c) ÷ 2, then A = √(s(s−a)(s−b)(s−c)). For the 3-4-5 right triangle, s = 6 and A = √(6 × 3 × 2 × 1) = √36 = 6 — matching ½ × 3 × 4, since the legs of a right triangle act as base and height. One note on wording: a flat triangle has area, not “surface area” — that term belongs to 3-D solids, though the math here is what you’d use for each triangular face.
How it’s calculated
Base-height mode: Area = ½ × b × h, where h is the perpendicular distance from the base to the opposite vertex. Heron mode: with sides a, b, c and semiperimeter s = (a + b + c) ÷ 2, Area = √(s(s−a)(s−b)(s−c)); the sides are first checked against the triangle inequality. Both methods are exact and unit-agnostic — results carry the square of the input unit.
Results update as you type and are estimates, not professional advice — verify important decisions with a qualified professional.
Common mistakes
- Forgetting the ½ — base × height alone is the area of the surrounding rectangle, twice the triangle.
- Using a slanted side as the height — h must meet the base at a right angle, so measure the perpendicular drop.
- Giving Heron’s formula three sides that can’t form a triangle (like 1, 2, 10) — each pair must sum to more than the third side.
Frequently asked questions
What is the area of a triangle formula?
A = ½ × base × height, with the height perpendicular to the base. A base of 10 and height of 6 give an area of 30.
How do I find the area of a triangle with 3 sides only?
Use Heron’s formula: s = (a + b + c) ÷ 2, then A = √(s(s−a)(s−b)(s−c)). Sides 3, 4, 5 give s = 6 and A = √36 = 6.
Does the formula work for every type of triangle?
Yes — right, isosceles, scalene, or obtuse. In an obtuse triangle the perpendicular height may fall outside the triangle, but ½ × b × h still gives the exact area.
Is the surface area of a triangle the same as its area?
For a flat 2-D triangle, yes — people say “surface area” loosely. Strictly, surface area describes 3-D solids, where you’d sum the area of each face.
What units is triangle area measured in?
The square of whatever you measure the sides in: inches give square inches, meters give square meters. Mixing units within one triangle breaks the result.