Volume & Surface Area Calculator
Calculate the volume and surface area of any solid — cube, box, sphere, cylinder, cone, pyramid, torus, capsule. Free, runs in your browser.
Volume and Surface Area Calculator
How to Use the Volume & Surface Area Calculator
Pick a solid
Choose from cube, box, sphere, cylinder, cone, square pyramid, torus, or capsule.
Enter the dimensions
The boxes adapt to the solid — a radius and height for a cylinder, three sides for a box, and so on. Type your measurements.
Read volume and surface area
Both appear instantly. Volume comes out in cubic units, surface area in square units — in whatever units you entered.
Use the numbers
Volume tells you capacity (litres, fill, material); surface area tells you covering (paint, wrap, sheet metal). Switch solids any time.
Volume and Surface Area in 3D
Capacity and Covering
Moving from flat shapes to solid ones brings two new questions: how much fits inside (the volume) and how much skin wraps around it (the surface area). Volume is what you need for capacity — the litres a tank holds, the concrete to fill a footing, the material in a part. Surface area is what you need for covering — the paint for a sphere, the metal to make a can, the wrapping for a parcel, the heat a body radiates. Each solid has its own pair of formulas, and they range from the simple (a cube's volume is just its side cubed) to the elegant (a sphere's volume is ⁴⁄₃πr³ and its surface 4πr²) to the genuinely intricate (a torus, the doughnut shape, or a capsule, a cylinder capped by two hemispheres). This calculator gathers the common solids in one place, changing its input boxes to suit whichever you pick, and gives both volume and surface area at once — no formula-hunting required.
One of the most important and counter-intuitive facts in all of geometry lives here: volume and surface area scale differently. If you double every dimension of a solid, its surface area goes up by a factor of four (two squared) but its volume goes up by a factor of eight (two cubed). This "square-cube law" is why a kitten cannot simply be scaled up into a lion's body plan, why large animals need proportionally thicker legs, why small creatures lose heat so fast, and why mixing, cooling, and chemistry all behave differently at different scales — the surface (where exchange happens) grows far slower than the volume (what has to be served). Seeing volume and surface area side by side, and being able to enter a solid and then a scaled-up version, makes this profound relationship concrete instead of abstract. It also explains everyday surprises, like why a large pot takes so much longer to cool than a small one.
"Double a solid's size and its surface grows fourfold but its volume eightfold. That square-cube law shapes everything from animal anatomy to why big things cool slowly."
From Tanks to Parcels
The practical reach of 3D measurement is enormous. Engineers size tanks, pipes, and pressure vessels; manufacturers calculate the material in a part and the coating to protect it; cooks and brewers work out the capacity of pots and fermenters; shippers compute the volume of parcels for freight and the surface for wrapping; and builders estimate concrete, fill, and insulation. The mix of solids matters because real objects are rarely simple — a storage tank is a cylinder with hemispherical or capsule ends, a hopper is a cone, a gear is close to a torus. Being able to switch solids in one tool, with the right inputs appearing automatically, turns a set of half-remembered formulas into a single reliable instrument. Because everything runs locally in your browser and is unit-agnostic, it is an instant, private way to get the two numbers most 3D projects need — capacity and covering — for the solid actually in front of you.
10 Facts About Volume & Surface Area
Volume is the space inside (cubic units); surface area is the skin around it (square units).
A sphere's volume is ⁴⁄₃πr³; its surface is 4πr².
Double a solid's size: surface ×4, but volume ×8 — the square-cube law.
That law is why small animals lose heat so quickly.
A cone holds exactly one-third of the cylinder around it.
A sphere has the least surface area for a given volume.
Archimedes found the sphere is two-thirds of its surrounding cylinder.
A torus (doughnut) and a capsule have their own neat formulas.
Volume gives capacity; surface area gives covering.
This tool covers eight solids with one shared, tested engine.
Frequently Asked Questions
- Choose Sphere and enter the radius. The calculator uses the formula ⁴⁄₃πr³ for the volume and 4πr² for the surface area, and shows both at once. For a radius of 3, the volume and surface area both come to about 113.1 (a happy coincidence that only occurs at r = 3).
- Volume is the amount of space inside a solid, measured in cubic units — it tells you capacity, like how much a tank holds. Surface area is the total area of the outside, measured in square units — it tells you covering, like how much paint or wrapping you need. The calculator gives both for every solid.
- Cube, box (cuboid), sphere, cylinder, cone, square pyramid, torus (ring/doughnut), and capsule. Picking a solid changes the input boxes to exactly the dimensions that solid needs, so you never enter anything irrelevant.
- When you scale a solid up, its surface area grows with the square of the scale factor but its volume grows with the cube. So doubling the size multiplies surface area by 4 and volume by 8. This explains why big animals need thick legs, small ones lose heat fast, and large objects cool slowly. Enter a solid, then a doubled version, to see it.
- A torus (doughnut) needs two radii: the major radius from the centre of the hole to the centre of the tube, and the minor radius of the tube itself — the tube radius must be smaller. A capsule is a cylinder with a hemisphere on each end, so you enter the radius and the straight cylinder height between the caps.
- Whatever units you enter. Measurements in centimetres give volume in cubic centimetres and surface area in square centimetres. Keep all the dimensions for one solid in the same units and the results are consistent.
- Yes — a cone with the same base radius and height as a cylinder has exactly one-third of its volume. You can verify it here: enter a cylinder and a cone with the same radius and height and compare the volumes. It is one of the most satisfying facts in solid geometry.
- Yes. The calculation runs in your browser — nothing is uploaded, stored, or logged — and it works offline once loaded.
- For flat shapes — squares, circles, triangles, polygons — use the Area & Perimeter Calculator, built on the same engine. This tool is for 3D solids; that one is for 2D shapes.
- Completely free, with no account, sign-up, or limit. It runs entirely in your browser and collects no data. Use it as often as you like.
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