Construction geometry
Triangle area from three sides
Calculate the area, perimeter and angles of a triangle from three measured side lengths.
Your inputs
Complete the fields for your selected method. Zero means intentionally zero, not unknown. Currency selection labels amounts; it does not convert exchange rates.
How this calculation works
Heron: area = sqrt(s × (s-a) × (s-b) × (s-c)), where s = (a+b+c)/2; angles use the cosine rule
Measurement arithmetic for the stated ideal shape. Verify dimensions and assumptions at the site. No structural sizing, code compliance, safe load, stair approval, accessibility certification or boundary survey is supplied. Straight sides and a flat triangle are assumed. Measurements close to a degenerate triangle are sensitive to small errors; independently verify site measurements. Side labels determine the opposite-angle labels.
What information do I need?
Use records for the same job, equipment or accounting period. Only the fields for your selected entry method are required. An unknown amount is not zero.
Input definitions and where to find them
- Side A (ft): Measure the stated distance and select its unit. Feet, inches and meters are supported. A perpendicular height is not a sloping length.
- Side B (ft): Measure the stated distance and select its unit. Feet, inches and meters are supported. A perpendicular height is not a sloping length.
- Side C (ft): Measure the stated distance and select its unit. Feet, inches and meters are supported. A perpendicular height is not a sloping length.
Use the Where to find this value controls beside the inputs for available work-it-out helpers. Estimates remain your assumptions; a helper does not verify the source figures.
Worked example
Example amounts use US dollars (USD).
Example answer: Triangle area is 6.0000 ft² for the illustrative inputs below.
Example inputs
- Side A: 3.00 ft
- Side B: 4.00 ft
- Side C: 5.00 ft
- Triangle area
- 6.0000 ft²
- Perimeter
- 12.0000 ft
- Angle opposite side A
- 36.8699 degrees
- Angle opposite side B
- 53.1301 degrees
- Angle opposite side C
- 90.0000 degrees
These illustrative values are not recommended rates or industry averages. Replace every example input with your own figures.
Use the result well
Calculate the area, perimeter and angles of a triangle from three measured side lengths.
Keep inputs on the same scope and time basis. Calculations retain precision internally; displayed values generally round to two decimal places, with extra precision for very small values and whole-unit rounding where required. Economic comparisons describe your supplied assumptions and do not guarantee future results.
This tool provides business arithmetic. It does not approve engineering designs, establish legal or tax treatment, select equipment or certify safe operating conditions.