About this calculator
The Trapezoid Calculator, also useful for the UK term trapezium, finds area from the two parallel sides and height. It can also calculate perimeter when both non-parallel side lengths are entered.
trapezoid calculator method
The area is the average of the two parallel sides multiplied by the height. Perimeter is the sum of all four sides.
- Area = (a + b) / 2 x h
- Perimeter = a + b + c + d
How to use the trapezoid calculator
- Enter the two parallel side lengths.
- Enter the vertical height.
- Optionally enter the two non-parallel side lengths.
- Average the parallel sides.
- Multiply by height for area.
- Add all four sides for perimeter if available.
Worked examples
Area only
Input: a = 12, b = 8, h = 5
Calculation: Area = (12 + 8) / 2 x 5
Result: 50 square units
Perimeter
Input: a = 12, b = 8, c = 6, d = 6
Calculation: P = 12 + 8 + 6 + 6
Result: 32 units
Trapezoid or trapezium
In US usage, trapezoid is common. In UK school maths, trapezium is often used for a quadrilateral with one pair of parallel sides. This page uses both terms for clarity.
Practical geometry checks
- Use one unit system
- Keep all lengths in the same unit before calculating. Mixing centimetres, metres, inches, or feet in the same formula will produce misleading results.
- Perimeter vs area
- Perimeter is a distance around the outside. Area is the amount of flat space inside a shape. Surface area is the total outside covering of a 3D shape.
- Rounded answers
- Pi, square roots, and trigonometric values are often irrational, so decimal answers are approximations. Keep extra decimal places until the final result.
Edge cases
- Zero or negative dimensions do not describe a real physical shape.
- Regular polygon formulas assume all sides and angles are equal.
- Circle and ellipse formulas use pi, so most decimal answers are rounded.
- A trapezoid/trapezium perimeter needs all four side lengths, not just the parallel sides and height.
Limitations
This calculator is for educational and planning use. For construction, manufacturing, surveying, engineering, or safety-critical work, confirm dimensions, tolerances, and rounding rules with the appropriate professional method or specification.
Frequently asked questions
What units should I enter?
Use any length unit you like, but keep every length in the same unit. If you enter metres, area is in square metres and surface area is also in square metres.
Why are some answers approximate?
Calculations involving pi, square roots, or curved shapes often produce irrational numbers. The calculator rounds the displayed decimal result.
What is the difference between area and surface area?
Area measures a flat 2D region. Surface area measures the total outside area of a 3D object.
Can I use these calculators for homework?
Yes. They are useful for checking answers and understanding formulas, but you should still show the working required by your class or exam.
Do regular polygon formulas work for irregular polygons?
No. Regular polygon formulas assume equal sides and equal angles. Irregular polygons usually need to be split into simpler shapes.
Related calculators
- Area Calculator
- Perimeter Calculator
- Polygon Calculator