📏 Enter known values

📐 Accepted units: mm, cm, dm, m, dam, hm, km, in, ft, yd, mi

Formula Reference

render

Worked example

Data
Height
\(b = {\color{#6c5ce7}{5\,\text{cm}}}\)
Length
\(c = {\color{#6c5ce7}{4\,\text{cm}}}\)
Width
\(d = {\color{#6c5ce7}{3\,\text{cm}}}\)
Volume
\(a = \,?\)
Formula
\[a = {b}\cdot{c}\cdot{d}\]
Steps
1Substitute the values
\[a = {\color{#6c5ce7}{5\,\text{cm}}}\cdot{\color{#6c5ce7}{4\,\text{cm}}}\cdot{\color{#6c5ce7}{3\,\text{cm}}}\]
Each letter is replaced by its value.
2Multiply
\[a = {\color{#6c5ce7}{5\,\text{cm}}}\cdot{\color{#6c5ce7}{4\,\text{cm}}}\cdot{\color{#6c5ce7}{3\,\text{cm}}} = 60\,\text{cm}^{3}\]
\(5\cdot4 = 20\)\(20\cdot3 = 60\)\(\text{cm} \times \text{cm} = \text{cm}^{2}\)\(\text{cm}^{2} \times \text{cm} = \text{cm}^{3}\)
Volume: 60 cm³
Check

If we use the result to calculate Height, we should get the value you entered:

\[b = \frac{{a}}{{c}\cdot{d}}\]
\[b = \frac{60\,\text{cm}^{3}}{4\,\text{cm}\cdot3\,\text{cm}} = 5\,\text{cm}\]
It gives 5 cm, the same as the value entered.
Calculate the Volume
Please fill in the fields:
Height Length Width
And leave empty
Volume
Calculate the Height
Please fill in the fields:
Volume Length Width
And leave empty
Height
Calculate the Length
Please fill in the fields:
Volume Height Width
And leave empty
Length
Calculate the Width
Please fill in the fields:
Volume Height Length
And leave empty
Width

How to calculate the volume of a rectangular prism

A rectangular prism (a box, or cuboid) has six rectangular faces. Its volume is the product of its three dimensions:

\[ V = \text{Length} \times \text{Width} \times \text{Height} \]

It is the area of the base (length × width) times the height. If you know the volume and two dimensions, divide to get the third one:

\[ \text{Height} = \frac{V}{\text{Length} \times \text{Width}} \]

How to use the calculator

  1. Enter three of the four values: the volume, the height, the length and the width.
  2. Leave empty the one you want to find.
  3. Press Calculate. Use the same unit for the three dimensions; the volume is in that unit cubed.

Worked examples

1. Box of 30 × 20 × 15 cm

\[ V = 30 \times 20 \times 15 = 9{,}000\ \text{cm}^3 = 9\ \text{L} \]

2. Fish tank

An aquarium 80 cm long, 35 cm wide and 40 cm tall holds \( 80 \times 35 \times 40 = 112{,}000\ \text{cm}^3 \), that is, 112 liters. Filled up to 35 cm, it holds 98 liters.

3. Concrete for a slab

A slab 5 m long, 4 m wide and 10 cm thick needs \( 5 \times 4 \times 0.1 = 2\ \text{m}^3 \) of concrete. Convert the thickness to meters before multiplying.

4. Height from the volume

A 60 L container (60,000 cm³) with a base of 50 × 30 cm is \( 60{,}000 \div (50 \times 30) = 40 \) cm tall.

Volume units

UnitEquivalent
1 cm³1 mL
1 dm³1 L = 1,000 cm³
1 m³1,000 L = 1,000,000 cm³
1 ft³28.32 L
1 in³16.39 mL

Other measurements of a box

  • Surface area: \( A = 2(LW + LH + WH) \).
  • Space diagonal: \( d = \sqrt{L^2 + W^2 + H^2} \), the longest straight object that fits inside.
  • A cube is a prism with three equal dimensions: \( V = a^3 \).

When Do You Need to Calculate the Volume of a Rectangular Prism?

📦 Moving and Shipping

Moving trucks, containers and couriers charge by volume. Measuring each box gives the space you need and the shipping cost.

Choose the right truck or package size
🐠 Aquariums and Tanks

The volume of a fish tank or a water tank tells you how many liters it holds, how much conditioner to add and how heavy it will be: 1 liter of water weighs about 1 kg.

Water volume, dosing and weight
🏗️ Concrete and Excavation

Slabs, footings and trenches are rectangular prisms. Their volume gives the cubic meters of concrete to order or of earth to dig.

Order concrete without running short
❄️ Heating and Air Conditioning

Heating and air conditioning are sized by the volume of air in a room: length × width × ceiling height.

Choose a unit of the right power
🌱 Raised Beds and Planters

Rectangular beds and planters are filled with soil by volume. Their volume tells how many bags of soil to buy.

Buy the right amount of soil
📚 Math and Science

The volume of a box is the starting point for units of volume, density and capacity at school.

Practice with cubic units and conversions

Common Mistakes

⚠️ Adding Instead of Multiplying
Common Error: Adding the three dimensions. For a box of 30 × 20 × 15 this gives 65 instead of 9,000.
✅ Solution: Multiply the three dimensions
⚠️ Mixed Units
Common Error: A slab of 5 m × 4 m × 10 cm multiplied as 5 × 4 × 10 = 200, instead of 2 m³.
✅ Solution: Convert all dimensions to one unit before multiplying
⚠️ Confusing Volume and Surface
Common Error: Using 2(LW + LH + WH), which is the surface area, when the question asks for the capacity.
✅ Solution: Volume = L × W × H, in cubic units
⚠️ Outside Instead of Inside Dimensions
Common Error: Measuring a tank or a box from the outside. The walls reduce the real capacity.
✅ Solution: Measure the inside to know the capacity
⚠️ Wrong Liter Conversion
Common Error: Treating 1 m³ as 100 L, or 1 L as 100 cm³.
✅ Solution: 1 L = 1,000 cm³ and 1 m³ = 1,000 L
⚠️ Filling to the Brim
Common Error: Calculating the capacity of a tank or a planter to the very top when it is never filled all the way.
✅ Solution: Use the real fill height

Applications by Industry

Logistics & Shipping
  • Containers: Cargo volume in containers and trucks
  • Couriers: Volumetric weight of packages
  • Warehouses: Storage capacity of shelves and pallets
Construction
  • Concrete: Volume of slabs, beams and footings
  • Excavation: Earth removed from trenches and pits
  • Materials: Volume of bricks and blocks
Heating & Air Conditioning
  • Rooms: Air volume to size heating and cooling
  • Ventilation: Air changes per hour
  • Ducts: Volume of rectangular ducts
Aquariums & Water Storage
  • Fish tanks: Liters of water and treatment doses
  • Cisterns: Capacity of rectangular cisterns
  • Pools: Water in rectangular pools with a flat bottom
Manufacturing & Packaging
  • Boxes: Box sizes for products
  • Molds: Material for rectangular molds
  • Stock: Volume and weight of metal blocks
Education
  • Geometry: Volume as base area × height
  • Physics: Density = mass ÷ volume
  • Units: Converting between cm³, liters and m³

External Resources

Other calculators

Volume of a Sphere
Volume of a Sphere
Volume of a Cube
Volume of a Cube
Volume of a Pyramid
Volume of a Pyramid
Volume of a Cylinder
Volume of a Cylinder
Volume of a Cone
Volume of a Cone
Volume of a Square Prism
Volume of a Square Prism
Surface Area of a Cylinder
Surface Area of a Cylinder
Internal Angles of a Quadrilateral
Internal Angles of a Quadrilateral

Geometry Calculators

Share this page with more people