Volume Calculator

Find the volume of a cylinder, cube, box, sphere, or cone from its dimensions, with results in cubic units, liters, and gallons.

Last updated:

Was this calculator helpful?

★ ★ ★ ★ ★
Embed this calculator

Calculation Examples

Calculation Case Result
Cylinder: radius 3 m, height 5 m Volume = 141.37 m³
Cube: side length 4 cm Volume = 64 cm³
Sphere: radius 6 cm Volume = 904.78 cm³
Mihail Doncenco
Mihail Doncenco Site Creator & Calculator Expert

Founder and developer of CalcMate. Builds and maintains every calculator on this site, focusing on formula accuracy and clear, practical results.

How to Use the Volume Calculator

Pick a shape from the menu, then enter its dimensions. A cylinder needs radius and height, a cube needs one side, a box (rectangular prism) needs length, width, and height, a sphere needs the radius, and a cone needs base radius and height.

Choose your unit (meters, centimeters, inches, or feet) and click "Calculate." The result appears in cubic units, plus liters and US gallons so you can match it to a tank label or a fill specification. Use the same unit for every dimension, and enter the radius, not the diameter.

Volume Formulas Explained

Each formula comes from integral calculus, adding up thin slices of the shape. Cylinder: \(V = \pi r^2 h\), where \(r\) is the base radius and \(h\) is the height. Cube: \(V = s^3\), where \(s\) is the side length. Rectangular prism: \(V = l \times w \times h\). Sphere: \(V = \dfrac{4}{3}\pi r^3\). Cone: \(V = \dfrac{1}{3}\pi r^2 h\), exactly one third of a cylinder with the same base and height. Archimedes showed in the 3rd century BC that a sphere fills two thirds of the smallest cylinder around it: \(V_{cylinder} = \pi r^2 \times 2r = 2\pi r^3\) and \(V_{sphere} = \dfrac{4}{3}\pi r^3\). The Roman writer Cicero reports that a sphere inside a cylinder marked his tomb. The calculator uses full-precision \(\pi\), not 3.14.Volume formulas for cylinder, cube, sphere, cone, and rectangular prism

Useful Tips 💡

  • For cylinders, spheres, and cones, enter the radius (half the diameter), not the diameter. A diameter typed as a radius makes a cylinder result four times too large and a sphere result eight times too large.
  • Convert everything to one unit first. A tank 50 cm wide and 1.2 m tall should be entered as 0.5 m and 1.2 m, or 50 cm and 120 cm, never 50 and 1.2 together.

📋Steps to Calculate

  1. Select the shape from the dropdown menu.

  2. Enter the dimensions (radius, height, side length, or length, width, and height).

  3. Select the unit of measurement and click "Calculate" to see the volume in cubic units, liters, and gallons.

Mistakes to Avoid ⚠️

  1. Entering the diameter instead of the radius. Because the radius is squared in a cylinder and cubed in a sphere, the result comes out 4 times and 8 times too large.
  2. Cubing the wrong thing in the sphere formula. The volume is four thirds times pi times r cubed, not r squared. Using r squared gives an area, not a volume.
  3. Using slant height instead of vertical height for a cone. A cone with radius 3 cm, true height 4 cm, and slant height 5 cm holds 37.7 cm³, but the slant value gives 47.1 cm³, which is 25% too large.
  4. Mixing up cubic centimeters and liters. One liter is 1,000 cm³, not 100, so a 500 cm³ container holds 0.5 liters, not 5.

Practical Applications📊

  1. Size a tank: a cylindrical tank with a 3 m radius and 5 m height holds about 141.4 m³, or 141,372 liters.

  2. Order concrete for a slab: 4 m by 3 m by 0.15 m is 1.8 m³. Add a margin for waste and uneven ground (5% to 10% is a common allowance), so order about 1.9 to 2.0 m³.

  3. Size a spherical tank: a sphere with a 3 m radius holds about 113.1 m³ (113,097 liters), and no other shape of that volume needs less wall material.

  4. Estimate a gravel pile: a cone-shaped pile with a 2 m base radius and 1.5 m height holds about 6.28 m³, one third of the 18.85 m³ cylinder with the same base and height.

Questions and Answers

Does the volume calculator handle unit conversions automatically?

Yes, it converts the result for you, but you must enter every dimension in the same unit. Choose the input unit (meters, centimeters, inches, or feet) and the calculator returns the matching cubic unit (m³, cm³, in³, or ft³), plus liters and US gallons. If your measurements come in different units, for example a radius in inches and a height in centimeters, convert them to one unit first. A radius of 10 and a height of 50 only mean something if both are in centimeters or both in inches.

How do you calculate the volume of a cylinder?

The volume of a cylinder is \(V = \pi r^2 h\), where \(r\) is the base radius and \(h\) is the height (or the length of a horizontal pipe). A cylinder with radius 0.5 m and height 2 m has \(V = \pi \times 0.25 \times 2 \approx 1.571\ \text{m}^3\), or 1,571 liters. The most common error is entering the diameter as the radius. Because the radius is squared, a 1 m diameter typed as a 1 m radius gives \(\pi \times 1 \times 2 \approx 6.283\ \text{m}^3\), four times too large. Halve the diameter first.

How do you calculate the volume of a sphere?

The volume of a sphere is \(V = \dfrac{4}{3}\pi r^3\), where \(r\) is the radius. A sphere with radius 5 cm has \(V = \dfrac{4}{3} \times \pi \times 125 \approx 523.60\ \text{cm}^3\). The radius is cubed, so measurement error grows fast: a 10% overestimate of the radius gives a 33.1% overestimate of volume, because \(1.1^3 = 1.331\). Measure the diameter at the widest point and halve it. For scale, Earth's mean radius of 6,371 km gives a volume of about \(1.083 \times 10^{12}\ \text{km}^3\).

How do you convert between cubic units and liquid volume units?

One liter equals 1,000 cm³ or 0.001 m³, so multiply cubic meters by 1,000 to get liters. One US liquid gallon is defined as exactly 231 cubic inches, which is 3.785411784 liters, so divide liters by 3.785 to get US gallons. One cubic foot is about 28.317 liters, and one cubic inch is 16.387 cm³ (exactly 16.387064, since 1 inch is exactly 25.4 mm). The UK imperial gallon is different at 4.546 liters, so check which gallon a specification uses.

How do you find the volume of a rectangular prism or box?

Multiply length by width by height: \(V = l \times w \times h\). A box measuring 40 cm by 30 cm by 20 cm has \(V = 40 \times 30 \times 20 = 24{,}000\ \text{cm}^3\), which is 24 liters. The formula works for any right-angled box, from shipping cartons and rooms to swimming pools approximated as rectangular blocks. For an L-shaped room or irregular container, split it into rectangular sections and add their volumes. Shipping carriers also use these dimensions to calculate dimensional weight when a package is light for its size.

What is a volume calculator and what shapes does it support?

A volume calculator finds the space inside a 3D shape from its dimensions. This one covers five shapes: cylinder, \(V = \pi r^2 h\); cube, \(V = s^3\); rectangular prism, \(V = lwh\); sphere, \(V = \dfrac{4}{3}\pi r^3\); and cone, \(V = \dfrac{1}{3}\pi r^2 h\). Results come in cubic units, with liters and gallons added for liquid capacity. Engineers use it to size tanks, builders to order concrete or gravel, and cooks and chemists to check container capacity.

What is the formula for the volume of a cone and how does it relate to a cylinder?

The volume of a cone is \(V = \dfrac{1}{3}\pi r^2 h\), exactly one third of a cylinder with the same base radius and height. You can check this by filling a cone with water and pouring it into a matching cylinder: it takes three fills. For a cone with base radius 4 cm and height 9 cm, \(V = \dfrac{1}{3} \times \pi \times 16 \times 9 \approx 150.80\ \text{cm}^3\). Use the vertical height from the base to the tip, not the slant length along the side. Cones appear in funnel and hopper design, gravel and grain piles, and volcano volume estimates.

What is the relationship between surface area and volume for common shapes?

Surface area measures the outer boundary in square units, and volume measures the interior in cubic units, so volume grows faster as a shape gets bigger. For a sphere, \(SA = 4\pi r^2\) and \(V = \dfrac{4}{3}\pi r^3\), which gives a surface-area-to-volume ratio of \(3/r\). For a cube, \(SA = 6s^2\) and \(V = s^3\), giving \(6/s\). Doubling the size of a shape cuts the ratio in half. That is why large animals lose heat more slowly than small ones, and why chemical reactors use fine powders to expose more surface per unit of material.
Disclaimer: This calculator is designed to provide helpful estimates for informational purposes. While we strive for accuracy, financial (or medical) results can vary based on local laws and individual circumstances. We recommend consulting with a professional advisor for critical decisions.