Volume Calculator Guide: Calculate Volume of Cylinders, Spheres & 3D Shapes
A volume calculator computes the volume of boxes, cylinders, cones, spheres, and tanks and converts between cubic units, liters, and gallons. It is useful for shipping, storage, aquariums, and construction takeoffs.
What is Volume Calculator?
The volume calculator provides formulas for common solids and supports unit conversions so you can switch between cubic centimeters, cubic inches/feet, liters, and gallons without losing precision.
How to Use the Volume Calculator
- Choose a shape (box, cylinder, cone, sphere, prism, tank).
- Enter dimensions (radius/diameter, length, width, height).
- Calculate volume and convert units if needed.
- For tanks, choose orientation (horizontal cylinder) and fill level to compute partial volume.
- Export results for quotes or materials planning.
Formulas & Methods
- Box/rectangular prism:
V = L*W*H. - Cylinder:
V = pi*r^2*h. - Cone:
V = (1/3)*pi*r^2*h. - Sphere:
V = (4/3)*pi*r^3. - Ellipsoid:
V = (4/3)*pi*a*b*c. - Tank partials: integrate area by fill height; the tool uses established segment formulas for horizontal cylinders and rectangular tanks.
- Conversions:
1 m^3 = 1000 L;1 ft^3 = 28.3168 L = 7.48052 gal (US).
Assumptions & limitations
- Input dimensions must use consistent units.
- Partial volume formulas assume uniform cross-sections.
- Real tanks have wall thickness and fittings that reduce usable volume slightly.
Examples
Example A — Cylinder
r = 0.15 m, h = 1.2 m -> V = pi*(0.15^2)*1.2 = 0.0848 m^3 = 84.8 L.
Example B — Horizontal tank partial
Cylinder D = 36 in, L = 72 in, fill depth = 18 in (half full).
Volume = 0.5 * (pi*(D/2)^2*L) = 0.5 * 36,651 in^3 = 18,326 in^3 = 79.3 gal (US).
| Shape | Formula | Notes | |---|---|---| | Box | L x W x H | Rectangular rooms | | Cylinder | pi r^2 h | Pipes/tanks | | Cone | 1/3 pi r^2 h | Hoppers | | Sphere | 4/3 pi r^3 | Bubbles/balls |
Pro Tips & Best Practices
- Convert diameter to radius correctly (
r = D/2) before using formulas. - For partial tanks, measure fill height accurately; small errors swing volume.
- Use consistent units; convert early or at the end, not mid-formula.
- Keep a safety margin when estimating container capacity.
- Report to appropriate sig figs based on measurement accuracy.
Related Calculators
FAQ
Q: How do I calculate the volume of a box or room?
A: Use V = L x W x H. Convert to liters or gallons as needed using a unit converter.
Q: What about cylinders and cones?
A: Cylinder V = pi r^2 h; cone V = (1/3) pi r^2 h. Keep radius and height consistent.
Q: How do I handle irregular shapes?
A: Break the shape into standard solids and sum volumes or use displacement methods.
Q: How do I convert between cubic units and liters/gallons?
A: 1 m^3 = 1000 L; 1 ft^3 = 7.48052 gal (US).
Q: What precision should I use?
A: Match significant figures to input measurements; carry extra digits through intermediate steps.
Engineering note: Uses geometric formulas for ideal solids; assumes negligible wall thickness and perfect shapes.
Call to Action
Choose a shape, enter dimensions, and get volume instantly—convert to liters or gallons and estimate partial tank fills with confidence.