About this Triangle Calculator
Finding the area of a triangle is easy if you know the base and height ($ rac{1}{2}bh$). But what if you only know the lengths of the three sides? This calculator uses Heron's Formula to solve for area without needing the vertical height.
Who this calculator is for
- Students solving SSS triangle problems with Heron's formula.
- Anyone checking whether three side lengths can actually form a triangle.
- People comparing a general triangle with a right-triangle shortcut.
When to use it
- Use this calculator when you know all three side lengths of a triangle.
- Use it to verify triangle validity before using the area and perimeter results.
- Use it when you need a general triangle method instead of a right-triangle-only tool.
How to use this calculator
- Enter the length of Side A.
- Enter the length of Side B.
- Enter the length of Side C.
- The tool calculates the Area and Perimeter.
Key assumptions
- All three side lengths are entered in the same unit.
- The calculator uses Heron's formula, so it assumes the three numbers describe side lengths rather than base-height data.
- If the side values are missing or non-positive, the calculator reports invalid input and does not return numeric results.
- If the triangle inequality is not satisfied, the triangle is marked as invalid geometry and numeric results are not returned.
Accuracy and testing
Review formula sources, default test cases, assumptions, unit handling, rounding rules, and changelog for this calculator.
How this calculator works
1. Calculate the Semi-Perimeter (s): $s = (a + b + c) / 2$
2. Calculate Area: $\sqrt{s(s-a)(s-b)(s-c)}$
This method works for any triangle (scalene, isosceles, or equilateral) as long as the side lengths are valid.
Inputs explained
Sides (a, b, c)
The lengths of the three edges of the triangle.
Understanding your results
If the output says 'No (Invalid Geometry)', the side lengths do not form a closed triangle. If it says 'Invalid Input', one or more side values are missing, non-numeric, or not positive.
Example scenarios
3-4-5 Triangle
Sides 3, 4, 5. Semi-perimeter = 6. Area = $\sqrt{6(3)(2)(1)} = \sqrt{36} = 6$.
Equilateral
Sides 5, 5, 5. Semi-perimeter = 7.5. Area ≈ 10.83.
Key Features
- Heron's Formula
- Geometry Validation
- Perimeter Calculation
Tips & Best Practices
- This is an SSS (Side-Side-Side) calculation.
- Ensure all side lengths are in the same unit (e.g., all meters or all inches).
Glossary of Terms
- Semi-Perimeter
- Half of the triangle's perimeter. A key variable in Heron's Formula.
- Triangle Inequality Theorem
- The rule that the sum of any two sides must be greater than the third side.