Calculator Form
Example Data Table
| Shape | Inputs | Formula | Volume |
|---|---|---|---|
| Cube | a = 4 cm | V = a³ | 64 cm³ |
| Cuboid | l = 8 m, w = 3 m, h = 2 m | V = l × w × h | 48 m³ |
| Cylinder | r = 3 cm, h = 10 cm | V = πr²h | 282.743 cm³ |
| Cone | r = 5 in, h = 12 in | V = (1/3)πr²h | 314.159 in³ |
| Sphere | r = 5 cm | V = (4/3)πr³ | 523.599 cm³ |
| Ellipsoid | a = 3 m, b = 2 m, c = 1 m | V = (4/3)πabc | 25.133 m³ |
Formula Used
Cube: V = a³
Cuboid: V = l × w × h
Cylinder: V = πr²h
Cone: V = (1/3)πr²h
Sphere: V = (4/3)πr³
Hemisphere: V = (2/3)πr³
Triangular Prism: V = (1/2) × b × h × L
Rectangular Pyramid: V = (l × w × h) / 3
Frustum of Cone: V = (1/3)πh(R² + Rr + r²)
Ellipsoid: V = (4/3)πabc
Keep all dimensions in the same linear unit. The output is always cubic, such as cm³, m³, in³, or ft³.
How to Use This Calculator
- Select the solid shape from the shape list.
- Choose one linear unit for every dimension.
- Enter the required values for that shape.
- Set the decimal precision you want displayed.
- Press Calculate Volume to show the result above the form.
- Review the formula, input summary, and scaling graph.
- Use the CSV or PDF buttons to export the result.
FAQs
1. Why is the output shown in cubic units?
Volume measures occupied space in three dimensions. Because length is multiplied three times, the result becomes cubic, such as cm³ or m³.
2. Can I mix units in one calculation?
No. Convert every dimension to the same unit first. Mixing cm, m, and inches in one formula will produce incorrect results.
3. What does the scaling graph represent?
It shows how volume changes when every dimension grows or shrinks by the same factor. Doubling all lengths increases volume eight times.
4. Which radius is used for spheres and cones?
Use the radius, not the diameter. If you only know the diameter, divide it by two before entering the value.
5. What is meant by semi-axes in an ellipsoid?
Semi-axes are the distances from the center to the surface along the three main directions. They are half of the full axis lengths.
6. Can this tool help with tank capacity estimates?
Yes. Choose the closest geometric shape, enter internal dimensions, and read the resulting volume. Then convert to liters or other capacity units if needed.
7. Why does a frustum need two radii?
A frustum is a cone with the top removed. The top and bottom circular faces have different radii, so both values are required.
8. Is this calculator useful for school and engineering work?
Yes. It supports common academic solids and practical estimation cases, making it helpful for maths practice, storage checks, and design calculations.