Volume Calculator
Calculate the volume of a cylinder, box, sphere, cone, pyramid, or capsule in any unit, with the formula and every common unit conversion shown.
كيفية استخدام هذه الحاسبة
- 1Pick the shape that matches what you are measuring.
- 2Choose the unit you measured in — every dimension must use the same one.
- 3Enter the dimensions. Radius is half the diameter, so measure across and halve it.
- 4Read the volume in your unit, and use the conversion table for litres, gallons, or cubic feet.
طريقة الحساب
Volume formulas
Cylinder V = π r² h Box V = l × w × h Sphere V = 4/3 π r³ Cone V = 1/3 π r² h Pyramid V = (l × w × h) ÷ 3 Capsule V = π r² h + 4/3 π r³
Every prism-like shape follows the same idea: the area of the base multiplied by the height. A cylinder is a circle of area πr² extruded through height h. Shapes that taper to a point — cones and pyramids — hold exactly one third of the prism that would enclose them, which is why the same formula appears divided by three. A capsule is simply a cylinder with a full sphere split across its two domed ends.
مثال محلول
A cylindrical tank with a 6-inch radius and a 12-inch height holds π × 6² × 12 = 1,357.17 cubic inches. That is 22.24 litres, or about 5.87 US gallons.
Volume Calculator: الدليل الكامل
Radius, not diameter
The single most common mistake in a cylinder calculation is entering the diameter where the radius belongs. Because the radius is squared, using the diameter by accident gives an answer four times too large.
Measuring across the widest part of a circular opening gives the diameter; halve it for the radius. If you have the circumference instead, divide it by 2π (about 6.283) to get the radius.
Volume, capacity, and the units people actually order in
Volume and capacity are the same quantity in different vocabularies. Solid materials are usually sold by cubic yards or cubic metres — concrete, gravel, topsoil, mulch. Liquids are sold in litres or gallons. Shipping and HVAC work in cubic feet.
The conversion table above gives all of them at once so the number can go straight into an order. Useful anchors: one cubic foot is about 7.48 US gallons, one cubic metre is exactly 1,000 litres, and one cubic yard is 27 cubic feet.
Why cones and pyramids are one third
A cone fits inside a cylinder of the same base and height, and a pyramid fits inside a matching box. In both cases the tapered shape occupies exactly one third of the enclosing solid — a result Archimedes proved geometrically and calculus reproduces in a line of integration.
This is worth remembering as a sanity check: if your cone volume is anywhere near the cylinder volume rather than a third of it, the divide-by-three has been dropped.
Partially filled tanks
A vertical cylinder filled to depth d holds πr²d — simply substitute the fill depth for the full height. A horizontal cylinder is much harder, because the cross-section of the liquid is a circular segment rather than a rectangle, and the volume is not proportional to the depth.
For horizontal tanks, a dipstick chart supplied by the manufacturer is more reliable than a formula. As a rough guide, a horizontal cylinder filled to half its diameter holds exactly half its capacity, but a quarter-depth fill holds only about 19%, not 25%.
الأسئلة الشائعة
How do I find the volume of a cylinder?
Multiply π by the radius squared by the height: V = πr²h. The radius is half the diameter. Every dimension must be in the same unit, and the answer comes out in that unit cubed.
How many gallons is a cubic foot?
One cubic foot is approximately 7.48 US gallons, or 28.32 litres. The conversion table above converts your result to gallons, litres, and cubic metres automatically.
Can I mix units, like feet and inches?
No — convert everything to a single unit first. A dimension of 5 feet 6 inches becomes 5.5 feet or 66 inches. Mixing units is the second most common source of wrong answers after diameter-versus-radius.
What is the volume of a capsule used for?
Capsule geometry describes propane tanks, pressure vessels, some water tanks, and pharmaceutical capsules. It is a cylinder with a hemisphere on each end, and the two hemispheres together make one complete sphere — which is why the formula adds a full 4/3πr³.