Triangle Area Calculator (3 Sides)
Enter the three side lengths below. This calculator uses Heron’s Formula to compute the area.
How to find triangle area from 3 sides
If you know all three side lengths of a triangle, you can find the area without needing the height. The standard method is Heron’s Formula, which is perfect for scalene, isosceles, and equilateral triangles.
Heron’s Formula:
s = (a + b + c) / 2
Area = √(s(s - a)(s - b)(s - c))
Step-by-step method
- Add the three sides to get the perimeter: a + b + c.
- Divide by 2 to get the semi-perimeter: s.
- Substitute into √(s(s-a)(s-b)(s-c)).
- Take the square root to get the triangle’s area.
Example calculation
Suppose sides are 13, 14, and 15 units.
- s = (13 + 14 + 15) / 2 = 21
- Area = √(21 × (21-13) × (21-14) × (21-15))
- Area = √(21 × 8 × 7 × 6) = √(7056) = 84
So, the area is 84 square units.
Important validation: triangle inequality
Three numbers only form a valid triangle if each pair of sides adds up to more than the third side:
- a + b > c
- a + c > b
- b + c > a
This calculator checks that rule automatically and will show an error if the side lengths are invalid.
Common mistakes to avoid
- Using negative or zero side lengths.
- Mixing units (for example, cm and m in the same triangle).
- Ignoring the triangle inequality check.
- Rounding too early during manual calculation.
Where this is useful
Finding area from three sides appears in geometry classes, engineering sketches, land surveying, construction planning, and computer graphics. Anytime side lengths are known but height is not, this method is efficient and reliable.
Quick FAQ
Can I use decimals?
Yes. Decimal values are fully supported.
What units does the result use?
The result is shown in square units of whatever unit your sides use (e.g., meters gives square meters).
Does this work for all triangle types?
Yes, as long as the three side lengths form a valid triangle.