Calculate the area of a triangle from a base and perpendicular height, or from three known sides with Heron’s formula.
Calculations happen locally. We do not send your values to our server.
A base of 10 with a height of 6 gives an area of 30, and a base of 7.5 with a height of 4 gives 15. From three sides, 3, 4 and 5 give an area of 6, while 7, 8 and 9 give about 26.83281573.
In base-height mode the area is base × height ÷ 2. In three-side mode the tool finds the semiperimeter s, half of the perimeter, and takes √(s(s−a)(s−b)(s−c)), which is Heron’s formula. Sides 5, 5 and 6 have a semiperimeter of 8 and an area of 12, and the semiperimeter is shown with the result.
The height is measured at a right angle to the base, not along a sloping side, and for an obtuse triangle it can fall outside the triangle on an extension of the base line. Use one unit for every length; the area then comes out in that unit squared. A height of 0 is accepted and gives an area of 0.
In base-height mode, enter any side as the base and the perpendicular distance from that side to the opposite corner as the height. A base of 10 with a height of 6 gives an area of 30, and a base of 7.5 with a height of 4 gives 15. The height is not the length of a sloping side; it is measured at a right angle to the base, and for an obtuse triangle it can fall outside the triangle on an extension of the base line.
When you know all three sides but no height, choose the three-sides method. The calculator finds the semiperimeter s, half the perimeter, and then takes √(s(s−a)(s−b)(s−c)). Sides 3, 4 and 5 give s = 6 and an area of 6; sides 5, 5 and 6 give s = 8 and an area of 12; sides 7, 8 and 9 give s = 12 and an area of about 26.83281573. This is useful for a triangular garden bed or roof section measured with a tape but without a square.
Any two sides must add up to more than the third, so 1, 2 and 3 is rejected: those lengths lie flat on a line and enclose no area. In base-height mode a height of 0 is accepted and returns an area of 0. Use one unit for every length; the area is then in that unit squared, such as m² for meters. For an irregular plot, split it into triangles along its diagonals, calculate each part and add the areas.
| Input | Result |
|---|---|
base 10 · h 6 | 30 |
base 7.5 · h 4 | 15 |
3, 4, 5 | 6 (s 6) |
5, 5, 6 | 12 (s 8) |
7, 8, 9 | 26.83281573 (s 12) |
Use base and height when you can measure a perpendicular, such as a drawing with a right angle marked. Use three sides when you have only a tape measure, for example a triangular garden bed or a roof section, since Heron’s formula needs no angle at all.
Any two sides must add up to more than the third. Lengths of 1, 2 and 3 lie flat on a line and enclose no area, so they are rejected rather than returning 0. Check your measurements when this happens; a mistyped digit is the usual cause.
Split it into triangles along its diagonals, calculate each one and add the areas. Measuring the diagonals lets you use the three-side method throughout, without needing a square. Keep a sketch with each measurement written on it so the parts can be checked later.
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