Volume Calculator
Volume of a sphere, cylinder, cone, prism, pyramid or rectangular box online: the formula, a step-by-step calculation and liters. Cylinder volume, sphere volume — solved.
Why you need a volume calculator
Volume is one of the few quantities people actually need day to day: how much water fits the pool, how much paint the wall needs, how much concrete goes into the foundation, whether the box fits in the trunk, whether the jar of jam lasts until winter. The formulas are simple, but it is easy to mix up radius with diameter and forget the third — the volume of a sphere or a cone differs from a cylinder by exactly that share. Doing volume by hand means working out every time which formula belongs to which shape, and then wondering which units the answer came out in. The calculator below handles each shape, shows the formula and breaks the calculation into steps, and converts the result into cubic centimeters and liters — because volume is sold in liters in the shop, while drawings quote it in cubic meters. There is one subtlety that trips people up more than any other: for a prism or a pyramid you do not enter a radius or a side length, but the already-computed area of the base. If the base is a 12 × 4 cm rectangle, work out the area first (four multiplications, no drama) and feed that number into the "Base area" field along with the height. A rectangular box is simpler still: the three edges multiply directly. And about units. The calculator accepts dimensions in centimeters, meters or millimeters and converts the result into cubic centimeters and liters on its own. That is convenient, but remember how the conversions relate: cubic centimeters and liters differ by a factor of 1000, and cubic meters by a factor of a million. A slip in the exponent is expensive, so type the dimensions exactly as the drawing states them and do not do the arithmetic in your head. If you need the base area along the way, reach for the area calculator, and for switching between centimeters and meters there is the unit converter.
What the volume calculator does
- Sphere, cylinder, cone, prism, pyramid and rectangular box — six shapes. Each has its own formula, and the right one is picked with a single button, with no page reload.
- A step-by-step calculation from the formula: you see what gets multiplied by what. For a sphere the substitution of the cubed radius is spelled out, for a cylinder r² and the height are listed separately, so a mismatch with your own arithmetic shows up immediately.
- The result straight in cubic centimeters, cubic meters and liters. Liters come from dividing by 1000, so a cylinder of 942.48 cm³ honestly reports 0.94 L.
- Input units: centimeters, meters or millimeters — the conversion to centimeters and liters is automatic. You never have to convert the dimensions to meters by hand.
- For prisms and pyramids you enter the finished base area, for a box its three edges. All dimensions must be positive; zero and negative values are rejected.
- Below the result block there is a separate reference card listing all six volume formulas — handy to keep in view while you check the result against a textbook or redo the arithmetic by hand. No signup and nothing is uploaded: the calculation runs entirely in the browser and the dimensions you type never leave the page.
How to calculate a volume
- Pick the shape with the buttons at the top of the block — the formula follows automatically. A sphere needs one radius, a cylinder and a cone need a radius and a height, a box needs all three edges.
- Enter the dimensions. For a cylinder, cone, prism and pyramid there are two fields: a radius and a height for the first two, a base area and a height for the last two. Values can be typed with a point or with a comma.
- Choose the units — centimeters, meters or millimeters — and read the result: the volume in your chosen units, the conversion into cubic centimeters and into liters, plus the formula broken down into steps.
- Sanity-check the order of magnitude. A sphere of radius 10 cm is 4188.79 cm³, that is about 4.19 L — four one-liter bottles. If your result is far smaller or larger, check whether a diameter went in where a radius belonged.
- Compare the result against a rounded reference point: a sphere of radius 10 cm is about 4.19 L, a cylinder of radius 5 and height 12 is just under a liter, and a cone with the same parameters is about 0.31 L. If your volume is off by a factor, check whether a diameter went in where a radius belonged.
Technical details
The school formulas are used: V = 4/3·π·r³ for a sphere, V = π·r²·h for a cylinder, V = 1/3·π·r²·h for a cone, V = S·h for a prism, V = 1/3·S·h for a pyramid and V = a·b·c for a box. Note the factor 1/3 on the cone and the pyramid — that is not an approximation or a rounding, but an exact ratio: a cone occupies precisely one third of the volume of a cylinder with the same base and height. On precision. π is taken from mathematics at full precision and rounding happens only at output: in the worked steps π is shown as 3.1416 and intermediate products (a squared radius, say) to hundredths, while the final figure is never longer than two decimal places. Converting to cubic centimeters multiplies by 10⁶ for meters and divides by 1000 for millimeters; dividing by 1000 gives liters, since one liter is exactly 1000 cubic centimeters. On number format. The final figure is printed with two decimal places, and whole values appear without a fractional part: 30,000 rather than 30,000.00. The intermediate steps are broken out separately, so you can re-do the multiplication by hand if you want to. On the limits. Every dimension must be strictly greater than zero — with a zero or a negative value no result is produced. A sphere needs only the radius, a cylinder, cone, prism and pyramid need a radius or base area plus a height, a box needs all three edges. An incomplete set of data never yields a "zero" result that could be mistaken for an answer. All computation runs in the browser, on your own device: the dimensions you type are never uploaded and never stored. At the bottom of the block all six formulas are collected in one list — handy for checking at a glance which of them applies to your shape.
Volume formulas and conversion to liters
| Shape | Volume formula | Example and result |
|---|---|---|
| Sphere | V = 4/3 · π · r³ | r = 5 cm → 523.6 cm³ (0.52 L) |
| Cylinder | V = π · r² · h | r = 5, h = 12 → 942.48 cm³ (0.94 L) |
| Cone | V = 1/3 · π · r² · h | r = 5, h = 12 → 314.16 cm³ (0.31 L) |
| Prism | V = S · h | S = 12, h = 4 → 48 cm³ (0.05 L) |
| Pyramid | V = 1/3 · S · h | S = 12, h = 4 → 16 cm³ (0.02 L) |
| Rectangular box | V = a · b · c | 40 × 30 × 25 → 30,000 cm³ (30 L) |
| Cone versus cylinder | V(cone) = V(cylinder) ÷ 3 | 942.48 ÷ 3 = 314.16 cm³ |
| Pyramid versus prism | V(pyramid) = V(prism) ÷ 3 | 48 ÷ 3 = 16 cm³ |
| Into cubic centimeters | m³ × 1,000,000 | 0.5 m³ → 500,000 cm³ |
| Into cubic meters | cm³ ÷ 1,000,000 | 30,000 cm³ → 0.03 m³ |
| Into liters | cm³ ÷ 1000 | 942.48 cm³ → 0.94 L |
| From millimeters | mm³ ÷ 1000 | 1000 mm³ → 1 cm³ |
| Sphere in liters | V = 4/3 · π · r³ | r = 10 cm → 4188.79 cm³ (4.19 L) |
| Cylinder in liters | V = π · r² · h | r = 3, h = 20 → 565.49 cm³ (0.57 L) |
| Box in liters | V = a · b · c | 60 × 40 × 35 → 84,000 cm³ (84 L) |
The volumes in the table are computed from the same formulas the calculator uses: π ≈ 3.1416, and the 1/3 factor on the cone and the pyramid is exact rather than approximate. Liters come from dividing cubic centimeters by 1000, cubic meters by dividing by a million.