Geometry

Triangle Area Calculator

What this does

Get triangle area from base and height, or from all three sides via Heron’s formula; no height needed.

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Calculator inputs

How to use it

Using the triangle area calculator

  1. 01

    Pick an input mode

    Base and height if you know them; three sides when you do not.

  2. 02

    Enter the lengths

    Any consistent unit; inches, meters, feet; just mix nothing.

  3. 03

    Read the area

    Returned in squared units; Heron mode also shows the semi-perimeter used.

Good to know

When Heron’s formula earns its keep

Surveyors, carpenters and game developers rarely have perpendicular heights handy but almost always know edge lengths. Heron converts three tape measurements into an exact area with no trigonometry required; a genuinely practical formula from antiquity.

Spotting invalid triangles early

If someone reports sides 2, 3 and 7, no triangle exists; the 2 and 3 cannot bridge the gap to 7. The inequality check catches typos before they contaminate material orders or land calculations.

How it's calculated

The math behind this calculator

A = ½·b·h Heron: A = √(s(s−a)(s−b)(s−c)), s = (a+b+c)/2

Base-and-height is the elementary formula: half the rectangle sharing those dimensions. Heron’s formula needs only side lengths, working through the semi-perimeter s; invaluable when the height cannot be measured directly, as with land plots defined by boundary stakes.

Heron mode validates the triangle inequality: each pair of sides must sum to more than the third. Violations describe impossible triangles and return an error rather than a nonsense number.

Assumptions & limitations

  • Base-height pairs must be perpendicular (h measured at right angles to b).
  • Heron mode requires sides satisfying the triangle inequality.
  • All lengths share one unit; area comes back in that unit squared.

Worked example

The classic 3-4-5 right triangle: using Heron’s formula, semi-perimeter s = 6 and the area works out to exactly 6 square units.

FAQ

Frequently asked questions

Does Heron work for right triangles too?
Yes; every valid triangle; 3-4-5 gives exactly 6 either way. Base-height may be faster when you already know both values.
Why did I get a triangle-inequality error?
Your three sides cannot close into a shape: the longest side equals or exceeds the other two combined. Check for typos or impossible measurements.
Is height always inside the triangle?
No; obtuse triangles have heights falling outside along an extended base. The formula still holds as long as you use the perpendicular distance.
How precise is Heron’s formula?
Mathematically exact; numerically it can lose precision on needle-thin triangles where s barely exceeds the longest side.

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