Unequal Triangle Area Calculator & Formula

This calculator works out the area of any triangle where the three sides are not equal (a scalene triangle). You enter the lengths of all three sides, and it returns the area in square units using Heron’s formula. It also gives the semi-perimeter, which is the intermediate value needed for the calculation.

Formula

Heron’s formula gives the area of a triangle when you know all three side lengths but not the height. It is:

Area = √(s × (s − a) × (s − b) × (s − c))

where:

• a, b, c = the lengths of the three sides (in any consistent unit, e.g., meters, feet, cm)
• s = semi-perimeter = (a + b + c) / 2 (same unit as the sides)

The result is in square units of whatever you used for the side lengths. If you input meters, the area is in square meters; if you input feet, the area is in square feet.

Worked Example

Using the default values from the calculator above: a = 5 m, b = 6 m, c = 7 m.

1. Calculate the semi-perimeter: s = (5 + 6 + 7) / 2 = 18 / 2 = 9 m
2. Apply Heron’s formula: Area = √(9 × (9−5) × (9−6) × (9−7))
3. Simplify inside the root: 9 × 4 × 3 × 2 = 216
4. Take the square root: √216 ≈ 14.6969 m²

The calculator rounds this to 14.70 m², matching the result shown.

When to Use This Calculator

Use this tool whenever you have a triangle with three known side lengths and none of them are equal. This is common in land surveying, construction, carpentry, and geometry homework. It is also useful for irregular plots of land that are triangular but not right-angled or isosceles.

If you only know two sides and the included angle, you would use the SAS formula (Area = ½ × a × b × sin(C)) instead. If you know the base and height, the simple ½ × base × height is faster. Heron’s formula is the most direct when you have all three sides and no angle or height.

How to Choose the Right Units

The calculator does not convert units for you. You must enter all three sides in the same unit. For example, if you have sides of 5 feet, 6 feet, and 7 feet, enter 5, 6, 7 and the area will be in square feet. If you mix meters and centimeters, the result will be meaningless.

Common unit pairs:

• Meters (m) → square meters (m²)
• Feet (ft) → square feet (ft²)
• Centimeters (cm) → square centimeters (cm²)
• Inches (in) → square inches (in²)

If you need the area in a different unit, convert the side lengths first, then calculate. For instance, to get square meters from feet, multiply each foot length by 0.3048 before entering.

Common Mistakes and Pitfalls

The most frequent error is entering sides that do not form a valid triangle. The triangle inequality states that the sum of any two sides must be greater than the third side. For example, sides of 1, 2, and 5 cannot form a triangle because 1 + 2 < 5. If you enter such values, the calculator will show an error or a negative number inside the square root (which is not a real area). Always check that your sides satisfy the inequality.

Another mistake is mixing units. Always convert all sides to the same unit before entering. Also, be careful with the order of operations when doing the calculation by hand: compute (s−a), (s−b), (s−c) first, then multiply, then take the square root.

Rounding too early can also cause small errors. Keep several decimal places during intermediate steps and round only the final area.

Limitations of Heron’s Formula

Heron’s formula works for every triangle that exists, but it is not always the most convenient. For very large or very small numbers, the multiplication inside the square root can overflow or underflow in a computer, but for typical real-world sizes this is not an issue.

Also, the formula gives the area, not the height or angles. If you need the height from a specific base, you would calculate area first, then use height = 2 × area / base. For angles, you would use the law of cosines.

For right triangles, the simpler formula (½ × base × height) is easier, but Heron’s formula will still give the correct answer.

Frequently Asked Questions

What is an unequal triangle called?

An unequal triangle is called a scalene triangle. It means all three sides have different lengths. Consequently, all three angles are also different.

Can I use this calculator for an isosceles triangle?

Yes. Heron’s formula works for any triangle, including isosceles (two equal sides) and equilateral (all equal). Just enter the three side lengths. For an equilateral triangle, you could also use the simpler formula (√3/4) × side², but this calculator will give the same result.

What if I only know two sides and the angle between them?

Then you cannot use Heron’s formula directly. You need the SAS formula: Area = ½ × a × b × sin(C), where a and b are the two sides and C is the included angle. You would need a different calculator for that.

Why does the calculator show an error for some side lengths?

Because those lengths do not form a valid triangle. The triangle inequality must hold: the sum of any two sides must be greater than the third. For example, 2, 3, and 6 cannot form a triangle because 2 + 3 < 6.

How do I convert the area to a different unit?

Convert the side lengths to the desired unit first, then recalculate. For example, to get square meters from square feet, divide the area by 10.7639, but it is safer to convert the sides and recalculate.

Does the order of the sides matter?

No. Heron’s formula is symmetric, meaning the area is the same regardless of which side you call a, b, or c. You can enter them in any order.

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in a | Side a | m | 5 | 0
in b | Side b | m | 6 | 0
in c | Side c | m | 7 | 0
out area | Area | m² | sqrt(s*(s-a)*(s-b)*(s-c)) | 2
out s | Semi-perimeter | m | (a+b+c)/2 | 2