Volume Calculator

The volume calculator works out how much three-dimensional space a solid object occupies, along with its surface area, for eight of the most common shapes you meet in school, college, and everyday work: the cube, cuboid, sphere, cylinder, cone, pyramid, ellipsoid, and torus. You pick a shape, choose a unit (millimetres through to yards), type in the measurements, and the result appears instantly in cubic units, with quick conversions to litres and US gallons alongside. It is built for CBSE, ICSE, and state-board students checking mensuration homework, for engineering and diploma learners, and for anyone practical — a plumber sizing a water tank, a farmer estimating a grain silo, a hobbyist filling an aquarium, or a homeowner ordering ready-mix concrete by the cubic metre.

What volume and surface area mean

Volume is the amount of space inside a solid, always measured in cubic units (cm³, m³, ft³ and so on) because it spans three directions: length, breadth, and height. Surface area is the total area of all the outer faces or curved surfaces wrapping the solid, measured in square units (cm², m²). You need volume to know capacity — how much water, sand, or air fits inside — and surface area to know how much paint, sheet metal, or wrapping is required to cover the outside.

The formulas, shape by shape

• Cube (all sides equal, length s): V = s³ and surface area = 6s².
• Cuboid (length l, width w, height h): V = l × w × h and surface area = 2(lw + wh + hl).
• Sphere (radius r): V = ⁴⁄₃πr³ and surface area = 4πr².
• Cylinder (radius r, height h): V = πr²h and total surface area = 2πr(r + h).
• Cone (base radius r, height h): V = ⅓πr²h and surface area = πr(r + l), where the slant height l = √(r² + h²).
• Pyramid (rectangular base l × w, height h): V = ⅓ × l × w × h.
• Ellipsoid (semi-axes a, b, c): V = ⁴⁄₃πabc.
• Torus (major radius R, minor radius r): V = 2π²Rr² and surface area = 4π²Rr.

The calculator uses the precise value of π (3.14159265…), so your answers are accurate to four decimal places rather than rounded to 22/7 or 3.14.

Worked example

Suppose you want the volume of a cylindrical overhead water tank with radius 0.5 m and height 1.2 m. Apply V = πr²h = π × (0.5)² × 1.2 = π × 0.25 × 1.2 = 0.3π ≈ 0.9425 m³. Because 1 m³ = 1,000 litres, that tank holds roughly 942 litres — close to the popular "1000-litre" Sintex size. The curved-plus-flat surface area is 2πr(r + h) = 2π × 0.5 × (0.5 + 1.2) = π × 1.7 ≈ 5.34 m², which tells you how much sheet you would need to fabricate it.

Tips for accurate results

• Keep every measurement in the same unit before you start; mixing centimetres and metres is the single biggest source of error.
• For a sphere, cylinder, or cone, enter the radius (half the diameter), not the full width across.
• To find capacity in litres, work in centimetres or metres — 1,000 cm³ = 1 litre, and 1 m³ = 1,000 litres.
• For real tanks and containers, the internal dimensions give usable capacity; the external dimensions give the material needed.

Common mistakes

The most frequent slip is using diameter where the formula expects radius, which inflates the answer four-fold for area and eight-fold for the volume of a sphere. Another is forgetting the ⅓ factor for cones and pyramids — both hold exactly one-third of the prism or cylinder that shares their base and height. A third trap is squaring instead of cubing, or vice versa: volume always carries a power of three across its length dimensions, while surface area carries a power of two. Finally, remember that unit conversion for volume is cubed: 1 m = 100 cm, but 1 m³ = 1,000,000 cm³, not 100 cm³. When in doubt, write out the formula with units attached and check that the final unit comes out as a cube (such as m³) for volume and a square (such as m²) for surface area before you trust the number.