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 this calculator effectively
This guide helps you use 3D Geometry Calculator in a repeatable way: define a baseline, change one variable at a time, and interpret outputs with explicit assumptions before you share or act on results.
How it works
The page applies deterministic logic to your inputs and shows rounded output for readability. Treat it as a comparison workflow: run one baseline case, adjust a single parameter, and measure both absolute and percentage deltas. If a result seems off, verify units, time basis, and sign conventions before drawing conclusions. This approach keeps your analysis reproducible across teammates and sessions.
When to use
Use this page when you need a fast estimate, a classroom check, or a practical what-if comparison. It works best for planning and prioritization steps where you need direction and magnitude quickly before investing in deeper modeling, manual spreadsheets, or formal external review.
Common mistakes to avoid
- Changing multiple parameters at once, which hides the true cause of output movement.
- Mixing units (percent vs decimal, monthly vs yearly, gross vs net) across scenarios.
- Comparing with another tool without aligning defaults, constants, and rounding rules.
- Using rounded display values as exact downstream inputs without re-checking precision.
Interpretation and worked example
Run a baseline scenario and keep that result visible. Next, modify one assumption to reflect your realistic alternative and compare direction plus size of change. If the direction matches your domain expectation and the size is plausible, your setup is usually coherent. If not, check hidden defaults, boundary conditions, and interpretation notes before deciding which scenario to adopt.
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.
How it's calculated
- Uses standard formulas for volume/surface area of sphere, cylinder, cone, prism/cuboid.
- Inputs validated as non‑negative; units carried consistently in output.
- Intermediate steps show substituted values when helpful.
- Share URL preserves parameters.