Geometry Calculator
One calculator for the most-asked geometry: the circumference and area of a circle, the volume of a cylinder, the Pythagorean theorem and the area of a triangle. Choose what you need, enter your measurements and see the formula and the answer straight away — so you also learn to work it out yourself.
Result
31.4159
Circumference
- Area
- 78.5398
- Diameter
- 10
How this was calculated
- 1Circumference2 × π × 5 = 31.4159
- 2Areaπ × 5² = 78.5398
Formula
Circle: C = 2πr, A = πr² · Cylinder: V = πr²h · Pythagoras: c = √(a²+b²) · Triangle: A = ½·b·h
For a circle you use the radius r and the constant π (≈ 3.14159): the circumference is 2πr and the area πr². A cylinder's volume is the circle's area times the height. The Pythagorean theorem gives the hypotenuse of a right triangle: c = √(a²+b²). A triangle's area is half the base times the height.
Step by step
- 1Choose the shape or theorem you need.
- 2Enter the first value (e.g. the radius) and, if needed, the second.
- 3Read the answer and the formula used.
Worked examples
Circumference of a circle with radius 5
→ 2 × π × 5 ≈ 31.42.
Pythagoras with a = 3 and b = 4
→ c = √(9 + 16) = 5.
Reference table
| Shape | Calculation | Formula |
|---|---|---|
| Circle — circumference | Circumference | 2πr |
| Circle — area | Area | πr² |
| Cylinder — volume | Volume | πr²h |
| Pythagoras | Hypotenuse | √(a²+b²) |
| Triangle — area | Area | ½·b·h |
r = radius, h = height, a and b = legs, b = base.
Common mistakes
- Confusing radius and diameter: the diameter is twice the radius.
- Forgetting to square for the area (πr², not πr).
- Applying Pythagoras to a non-right triangle.
When to use it
- Estimating the water in a round rain barrel (cylinder).
- Finding the length of a brace or ladder with Pythagoras.
- Calculating the area of a triangular plot or roof.
Frequently asked questions
How do I calculate the circumference of a circle?
Multiply the radius by 2 and by π: C = 2πr. With only the diameter, the circumference is π × diameter.
How do I calculate the volume of a cylinder?
Compute the circle's area (πr²) and multiply by the height: V = πr²h. If you work in cm, divide by 1000 for litres.
What is the Pythagorean theorem?
In a right triangle a² + b² = c², where c is the hypotenuse. So the hypotenuse is √(a²+b²).
How do I calculate the area of a triangle?
Multiply the base by the height and divide by 2: A = ½ × base × height.
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