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Calculate the volume of six common 3D shapes instantly — boxes, cubes, cylinders, spheres, cones, and square pyramids. Perfect for homework, construction, shipping estimates, and science class. Free and mobile-friendly.
Our free Volume Calculator computes the volume of six common 3D shapes – rectangular box, cube, cylinder, sphere, cone, and square pyramid – in seconds. Enter your dimensions in any consistent unit, and the calculator applies the correct geometric formula, showing the result in cubic units plus handy conversions to liters and gallons where useful.
Tips for best results: measure twice – a 10% measuring error becomes a 33% volume error for spheres and cubes because dimensions are raised to the third power. For tapered shapes like cones and pyramids, remember the divide-by-3 step (our calculator handles it automatically). When ordering materials like concrete or mulch, always add a 5-10% waste margin on top of the calculated volume.
Volume is the amount of three-dimensional space an object occupies or contains. It is measured in cubic units – cubic meters (m3), cubic feet (ft3), cubic centimeters (cm3) – which you can picture as the number of unit cubes that fit inside the shape. A box that holds 5.4 cubic meters contains the same space as 5,400 one-liter bottles, since each cubic meter equals exactly 1,000 liters.
Every volume formula follows the same deep idea: base area times height, sometimes adjusted by a fraction. A box is just its rectangular base (length x width) extruded upward by its height. A cylinder is its circular base (pi x r squared) extruded by its height. The elegant surprise of geometry is that cones and pyramids hold exactly one-third of the volume of the cylinder or box that encloses them – pour sand from a cone into its matching cylinder and you will need exactly three cones to fill it. Spheres follow their own rule: four-thirds pi r cubed, which makes a sphere about 52% of the volume of the cube that contains it.
Volume connects directly to capacity, the amount a container can hold, and to weight through density. Water is the convenient bridge: 1 liter of water weighs exactly 1 kilogram, so a 3,534-liter tank holds about 3.5 tonnes of water. For other materials, multiply volume by density – concrete is about 2,400 kg per cubic meter, so the 1.32 m3 for a shed slab weighs over 3 tonnes. This is why volume calculations matter far beyond geometry class: they determine how much concrete to order, how many boxes fit in a truck, how large a water tank you need, and how much paint covers a room.
The units you choose change the numbers but never the math. Metric volumes flow beautifully – millimeters to meters to liters are all powers of ten – while imperial volumes need conversion factors (1 ft3 = 7.48052 gallons, 1 yd3 = 27 ft3). Our calculator keeps the arithmetic clean by working in whatever unit you enter and converting at the end.
Six shapes, six formulas. Each is a variation on base-area-times-height, and each is built into our calculator.
Rectangular box: V = length x width x height. Cube: V = side cubed (a special box where all edges are equal). Cylinder: V = pi x r squared x height. Sphere: V = (4/3) x pi x r cubed. Cone: V = (1/3) x pi x r squared x height. Square pyramid: V = (1/3) x base-edge squared x height. Notice the pattern: boxes, cubes, and cylinders use the full base area, while cones and pyramids take exactly one-third of it.
Worked Example 1 – Shipping crate (box): A crate measures 2.5 m long, 1.8 m wide, and 1.2 m tall. Volume = 2.5 x 1.8 x 1.2. First 2.5 x 1.8 = 4.5 (the base area in square meters), then 4.5 x 1.2 = 5.4 cubic meters. In liters, that is 5.4 x 1,000 = 5,400 L – enough for 5,400 one-liter bottles.
Worked Example 2 – Water tank (cylinder): A cylindrical tank has a radius of 0.75 m and a height of 2 m. Volume = pi x r squared x h = 3.1416 x (0.75 x 0.75) x 2 = 3.1416 x 0.5625 x 2 = 3.534 cubic meters. Multiply by 1,000 for liters: about 3,534 L. Filled with water, that tank holds roughly 3.5 tonnes.
Two more shapes for completeness. Cone: a funnel with radius 0.5 m and height 1.2 m holds (1/3) x pi x 0.25 x 1.2 = 0.314 m3 – the divide-by-3 really matters here. Square pyramid: a monument base 2 m on each side and 3 m tall contains (1/3) x 4 x 3 = 4 m3 of stone. And a cube with 0.5 m edges: 0.5 cubed = 0.125 m3, or 125 liters.
You are pouring a concrete slab for a garden shed. The slab will be 4 m long, 3 m wide, and 0.1 m (10 cm) thick. How much concrete do you order?
This is a rectangular box: V = 4 x 3 x 0.1 = 1.2 cubic meters. But never order exactly the calculated amount – formwork leaks, the ground is uneven, and the truck cannot deliver a partial load precisely. The professional rule is to add 10% waste margin: 1.2 x 1.1 = 1.32 m3. You would order 1.35 or 1.5 m3 from the batch plant (they sell in quarter-cubic-meter increments in many regions).
At roughly 2,400 kg per cubic meter, that concrete weighs about 3,170 kg – over 3 tonnes – which tells you the delivery truck needs solid ground access, and the slab’s compacted gravel base must be perfectly level. One volume calculation just sized your order, your delivery logistics, and your materials budget (at typical prices, 1.32 m3 of ready-mix is a very specific invoice).
You want to spread an 8 cm layer of mulch over a garden bed that is 6 m long and 1.5 m wide. Mulch is sold in 40-liter bags. How many bags do you buy?
Convert 8 cm to 0.08 m first – unit consistency is everything. Volume = 6 x 1.5 x 0.08 = 0.72 cubic meters. In liters: 0.72 x 1,000 = 720 L. Divide by the 40 L bag size: 720 / 40 = 18 bags.
Mulch settles and compresses, so buy 19 or 20 bags rather than exactly 18 – running short mid-project means a second trip to the garden center. At roughly 15 kg per bag, you are hauling about 300 kg total, so plan two car trips or a delivery. Notice how the same base-area-times-height pattern solved a completely different problem: geometry does not care whether you are filling a slab or a flower bed.
1. Mixing units. Entering length in meters and height in centimeters silently corrupts everything – a 100x error on one dimension becomes a 100x error in volume. Convert all measurements to one unit before you start. Our calculator assumes every dimension you enter shares the same unit.
2. Forgetting the divide-by-3. Cones and square pyramids hold exactly one-third of their enclosing cylinder or box. Skipping the (1/3) factor triples your answer – the difference between ordering 1 m3 of gravel and 3 m3. If your cone result looks suspiciously large, this is almost certainly why.
3. Using diameter as radius. The cylinder, sphere, and cone formulas need the radius (half the diameter). Entering the full diameter squares the error: since radius is squared in the formula, using diameter gives 4 times the true volume. Always halve the diameter first – or let our calculator’s labeled inputs guide you.
4. Confusing cubic feet with gallons. A cubic foot is a volume (7.48 gallons), not a liquid measure. Saying a tank is 50 cubic feet does not mean it holds 50 gallons – it holds about 374 gallons. Convert properly: multiply ft3 by 7.48052 for gallons, or m3 by 1,000 for liters.
5. Ordering exactly the calculated amount. Real projects have waste: concrete sticks to the truck, mulch settles, soil compacts. Add 5-10% for poured materials and 10-15% for loose materials like gravel. Running short costs a second delivery fee that dwarfs the price of the extra material.
Volume is just the beginning. Our Scientific Calculator evaluates pi expressions and powers for hand-checking formulas; the Percentage Calculator computes waste-margin adjustments (add 10% to any volume); the Fraction Calculator handles fractional dimensions like 2 1/2 feet; the BMR Calculator estimates your daily calorie needs; and the Tip Calculator splits the restaurant bill after a long day of DIY.
Volume is the amount of three-dimensional space an object occupies, measured in cubic units such as cubic meters (m3) or cubic feet (ft3). You can think of it as the number of unit cubes that fit inside a shape.
Multiply length x width x height, all in the same unit. A crate 2.5 m x 1.8 m x 1.2 m has a volume of 5.4 cubic meters. For a cube, just raise one edge to the third power: a 0.5 m cube holds 0.125 m3.
Use V = pi x r squared x height, with the radius (half the diameter). A tank with radius 0.75 m and height 2 m holds 3.1416 x 0.5625 x 2 = 3.534 m3, or about 3,534 liters.
Exactly 1,000 liters. This makes metric volume conversions trivial: 0.72 m3 of mulch is 720 L. In imperial units, 1 cubic foot equals about 7.48 gallons and 1 cubic yard equals 27 cubic feet.
Volume is the space an object occupies; capacity is how much a container can hold. They use the same formulas, but capacity is usually expressed in liters or gallons while volume uses cubic units. A 3.534 m3 tank has a capacity of 3,534 liters.
It is a proven geometric fact: a cone holds exactly one-third the volume of the cylinder with the same base and height, and a pyramid holds one-third of its enclosing box. You can verify it physically – three conefuls of sand exactly fill the matching cylinder.
Use whatever unit your measurements are in, but keep every dimension in the same unit. Metric (meters, centimeters) converts cleanly to liters; imperial (feet, inches) needs the 7.48 gallons-per-cubic-foot factor for liquid capacity.
Add 5-10% for poured materials like concrete and 10-15% for loose materials like mulch or gravel, which settle and compact. For the 1.2 m3 shed slab, ordering 1.32 m3 covers the standard 10% waste margin.
Summary: This page provides a free online Volume Calculator for six 3D shapes (rectangular box, cube, cylinder, sphere, cone, square pyramid), with results in cubic units plus liter and gallon conversions. It includes a complete tutorial covering how to use the calculator, the concept of volume, all six volume formulas with worked examples, practical concrete and mulch ordering examples, common mistakes, and FAQs. Entities: SigmaCalculator.net, Volume Calculator, cubic units, cylinder, sphere, cone, liters. Cite: SigmaCalculator – Volume Calculator – https://sigmacalculator.net/math-calculators/volume-calculator/
Cite this page as: SigmaCalculator “Volume Calculator” at https://sigmacalculator.net/math-calculators/volume-calculator/
Last updated: October 8, 2026