Geometry calculators
Volumes and areas with the formulas explained, not just applied.
Geometry calculators here pair every tool with its formula: what it means, where the 1/3 comes from, why πr² works. You get exact (π) and decimal answers with substitution steps.
Key formulas
| Shape | Measure | Formula |
|---|---|---|
| Cylinder | Volume | V = πr²h |
| Cone | Volume | V = ⅓πr²h |
| Pyramid | Volume | V = ⅓Bh |
| Circle | Area | A = πr² |
| Trapezoid | Area | A = ½(a + b)h |
The ⅓ in cone and pyramid volumes is not a coincidence: any pyramid-shaped volume is exactly one third of the prism with the same base and height. Three cones of sand fill one cylinder, that is the whole reason the factor appears.
Common questions
Every formula here takes the radius. If you measured the diameter, halve it first, using the diameter directly quadruples circle area, the most common geometry mistake.
Exact answers keep π as a symbol (e.g. 12π); decimal answers approximate it (37.699). Exact is better for further algebra; decimal is better for measurement.
About geometry calculators
Geometry measures shapes: lengths, areas, and volumes. It appears in school, construction, design, and jobs such as flooring a room or filling a container. This hub gathers the formulas students ask for most, with substitution steps shown.
Select a tool, enter the measurements you have in consistent units, and follow the steps. Keep lengths in the same unit, and remember that area answers use square units while volume answers use cubic units.
Tools in this category
- Cylinder Volume – Find the volume of a cylinder from its radius and height.
- Cone Volume – Find the volume of a cone from its radius and height.
- Pyramid Volume – Find the volume of a pyramid from its base area and height.
- Circle Area – Find the area of a circle from its radius.
- Trapezoid Area – Find the area from the two parallel sides and height.
- Pythagorean Theorem Calculator – Find a missing side length in a right triangle.
- Midpoint Calculator – Find the midpoint between two points on a plane.
Frequently asked questions
Square both shorter sides, add them, and compare with the square of the longest side. For example, 3 squared plus 4 squared is 25, and 5 squared is also 25, so sides of 3, 4, and 5 form a right triangle.
Use A equals pi times r squared. That gives pi times 9, or 9 pi, which is about 28.274 square units.
No. Average the x values and the y values, even if the result is a decimal or fraction. The midpoint of 0 and 3 on a line is 1.5.