Math & Statistics Calculators · Geometry
Free Triangle Area Calculator for Base and Height, Heron Formula, SAS, and Coordinates
Find triangle area using the information you actually have: base and height, three side lengths, two sides with the included angle, or three coordinate points.
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Interactive calculator
Area—
Perimeter—
Altitude / extra—
Choose a method and enter values.
How to use it
- Choose the mode that matches the measurements you know.
- Enter only the values required for that mode.
- For SAS, supply the included angle between the two sides.
- For three sides, verify the sides satisfy the triangle inequality.
- Report area in squared units and lengths in linear units.
What this calculator includes
1. Base-height modeUse A = bh/2.
2. Heron modeCalculate area from three side lengths.
3. SAS modeUse two sides and included angle.
4. Coordinate modeUse the shoelace/determinant formula.
5. Triangle validityCheck side-length triangle inequality.
6. PerimeterCalculate when all three side lengths are known.
7. SemiperimeterShow s for Heron calculations.
8. AltitudeDerive altitude from area and selected base.
9. Unit-neutralSupports any consistent length unit.
10. Step breakdownShows the exact area formula used.
11. Local historySave recent triangle calculations.
12. Geometry examplesLoad common 3-4-5 and coordinate triangles.
Result checklist
0 / 5 complete
Local calculation history
Formula and reference table
| Method | Formula | Required inputs |
|---|---|---|
| Base/height | A = bh/2 | base, perpendicular height |
| Heron | A = √[s(s−a)(s−b)(s−c)] | three sides |
| SAS | A = ab sin(C)/2 | two sides + included angle |
| Coordinates | |x1(y2−y3)+…|/2 | three points |
Quick knowledge check
Which angle is required for the SAS area formula?
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Frequently asked questions
What if I only know three sides?
Use Heron mode. The calculator first verifies the triangle inequality, then computes semiperimeter and area.
Can I use coordinates?
Yes. Enter x and y for all three vertices and the determinant formula gives the area.
Why is height perpendicular?
Triangle area uses the shortest perpendicular distance from the chosen base line to the opposite vertex.
What units are returned?
Area is in squared units based on the input lengths.
Scope and accuracy
The calculator assumes planar Euclidean geometry. Very large, very small, or nearly degenerate triangles can be sensitive to floating-point rounding.