Compute the volume and surface area of spheres, cylinders, cones, rectangular prisms, and regular prisms. Ideal for architecture, fabrication, education, and lab work.
Your inputs sync to the query string, so you can share or reopen exact calculations on any device.
How to use the 3D geometry calculator
Choose the solid first, then enter dimensions in one unit system. The calculator reports volume and surface area from the same inputs, so a radius/diameter or height/slant-height mix-up will affect several results at once.
How it works
Each shape uses the standard formula for its geometry, with π kept internally and rounded only in the displayed answer. If you compare with a worksheet or CAD note, align whether the input is radius, diameter, edge length, perpendicular height, or slant height before judging a difference.
When to use
Use this page for quick classroom checks, packaging estimates, material takeoffs, and sanity checks before moving to a more detailed drawing. It is best for idealized shapes; irregular solids still need measurement or decomposition into simpler parts.
Common mistakes to avoid
- Entering a diameter where the form asks for a radius.
- Mixing centimeters, meters, inches, and feet in the same shape.
- Using slant height as vertical height for cones or pyramids.
- Rounding π or intermediate dimensions before comparing surface area and volume.
Interpretation and worked example
For a cylinder, enter radius and height in the same unit. Volume grows with radius squared, so doubling radius has a much larger effect than doubling height. If the output looks too large, check the radius/diameter distinction first, then confirm the unit shown beside each input.
See also
FAQ
How should I handle units?
Use the same unit for every dimension. Volume is returned in cubic units and surface area in square units.
Does the shared URL keep my inputs?
Yes. Values are stored in the query string so anyone opening the link will see the same setup.
What should I do first on this page?
Start with the minimum required inputs or the first action shown near the primary button. Keep optional settings at defaults for a baseline run, then change one setting at a time so you can explain what caused each output change.
Why does this page differ from another tool?
Different pages often use different defaults, units, rounding rules, or assumptions. Align those settings before comparing outputs. If differences remain, compare each intermediate step rather than only the final number.
How reliable are the displayed values?
Values are computed in the browser and rounded for display. They are good for planning and educational checks, but for regulated or high-stakes decisions you should validate assumptions with official guidance or professional review.
How it’s calculated
- Sphere: V = 4/3·π·r³ and A = 4·π·r².
- Cylinder: V = π·r²·h and A = 2·π·r·(r+h).
- Cone: V = 1/3·π·r²·h and A = π·r·(r+ℓ), where ℓ is the slant height.
- Prism: V = base area × height; surface area sums all faces.
- Outputs use square/cubic units consistent with your inputs.
- Symbols: V = volume, A = surface area, B = base area, Aₗ = lateral area, d = space diagonal, ℓ = slant height.