Solid Geometry Calculator
Find volume, surface area or a missing dimension. Check the labeled measurements and model before reuse.
Measure a solid
Example: a 2 × 3 × 4 cm box. Replace these measurements with yours.
How it works
Choose the geometric model before the formula
A right prism has joining edges perpendicular to its base planes. That is a different condition from having a right-angled triangle in the base. A centered pyramid places its apex directly above the base center. Choose those labeled methods only when they describe your solid. For an oblique prism or offset pyramid with known base area, use the general-volume method: perpendicular height still gives volume, while the exterior surface may remain undetermined.
Normalize the measurements, then calculate
Each length has its own unit. A box measuring 200 cm by 3 m by 4000 mm is 2 m by 3 m by 4 m, so its volume is 24 m³ and its closed surface is 52 m². Cubic conversion factors are the cube of length factors; square factors are squared. Changing a unit preserves the quantity. Fractions and explicit feet-plus-inches fields are supported, but unit text inside a scalar field is rejected.
Name the faces included in the surface
Closed total surface includes every face defined by the model. Open-top omits the named top base; lateral or curved surface omits bases. A tube’s annular ends are material rings, not plugs filling the bore. A joined solid hides contact faces, so adding component surface areas does not give its exterior. Check the selected boundary next to the result, the dimension table and the reusable report.
Common questions
Why can volume alone not determine a box?
Many different boxes have the same volume. To find one edge of a box you also need the other two independent edges. Choose a named inverse method and enter sufficient measurements; an empty field does not silently select an inverse. A cube is different because all three edges are equal. Its edge is the cube root of its volume. Surface-based inverses must use the closed total surface specified by that method.
Why do two spherical caps fit the same radii?
A plane can cut a sphere on either side of its center. With sphere radius 5 and circular-base radius 3, the cap heights are 1 and 9. Their volumes are 14π/3 and 162π. The calculator shows both possibilities and asks you to choose the cap matching your drawing. The same base and sphere radii do not determine which branch you intended.
Can I add volumes and surface areas in the same way?
Only nonoverlapping volumes can be added directly; cutouts must be contained and must not overlap one another. You supply that decomposition. Contact faces disappear inside joined objects and cutouts may reveal new faces, so this calculator does not infer arbitrary composite exterior surface. The defined coaxial cylinder–hemisphere preset has a known interface and can exclude that shared circular face explicitly.
Are measurements saved or placed in a share link?
The calculator uses temporary page memory. It does not save your measurements, put them in a share URL or send them to a calculation service. Copy, text download and print are actions you choose. If copying fails, open the report and select its text. Hosting still processes ordinary page requests under the site privacy policy; this is not a claim that the website processes no data.
Practical guides
- Read radius, height and axes in a solid diagram
Distinguish a radius from a diameter, perpendicular from total height and semiaxes from full axes before calculating.
- Convert cubic units and understand capacity
Work through mixed dimensions, square and cubic factors, liters and the two gallon systems.
- Find a missing dimension from volume or surface
Check sufficient givens and solve a named one-unknown geometry problem with a forward check.
- Add volumes and handle shared surfaces
Build a signed component audit while keeping spatial assumptions and exterior-surface limits visible.
- Pyramid volume: base area and perpendicular height
Use centered or general-base methods, distinguish face slant from perpendicular height and check an inverse.
Scope and limitations
Ideal declared geometry only. No structural, material-order, freight-fit, clinical or certified-capacity decisions. General-base volume can be valid while surface is undetermined. Numeric limits are software bounds, not measurement tolerances. Calculations stay in temporary page memory; no input share URLs or storage. Copy, download and print are optional local actions.