Volume of Rectangle
A rectangle extended into 3D space becomes a rectangular prism (cuboid). Adjust the dimensions below and watch the live 3D model update in real time.
Volume of Rectangle Definition
The volume of a rectangle is the total three-dimensional space enclosed inside a rectangular solid (rectangular prism or cuboid). A 2D rectangle has no volume — only area. When people search "volume of a rectangle," they mean a 3D rectangular box.
Volume quantifies the 3D space a substance occupies. The SI unit is the cubic meter (m³).
Volume differs from area. Area measures the 2D surface of a flat rectangle (m², cm², in²). Volume measures the 3D space inside a solid shape (m³, cm³, in³).
How to Calculate Volume of Rectangle?
To calculate the volume of a rectangle, multiply its length by its width by its height: V = l × w × h. All three measurements must be in the same unit.
Volume of Rectangle Formula
The volume of a rectangle formula is V = l × w × h, where V is the volume, l is the length, w is the width, and h is the height.
An alternative form uses the base area B = l × w:
Both forms produce identical results. Use V = B × h when the base area is already known.
The formula applies to any rectangular box: storage containers, rectangular tanks, bricks, rooms, and freight containers.
Volume of a Hollow Rectangle
Vhollow = (L × W × H) − (l × w × h)
Where uppercase = outer dimensions and lowercase = inner dimensions. Calculate each volume separately, then subtract.
Volume Without Height & With Depth
Without Height
If height is unknown, rearrange: h = V ÷ (l × w). Divide the known volume by the base area to find the missing height.
With Depth
V = l × w × d — "depth" replaces "height" as the third dimension. The calculation is identical; the term changes by context.
Three dimensions are always required. If two dimensions and the volume are known, any missing dimension can be solved algebraically.
Understanding Rectangular Solids & Prisms
A rectangular solid has 6 flat rectangular faces, 12 edges, and 8 vertices. Every pair of opposite faces is identical and parallel. All angles are 90°. Also called a cuboid. When l = w = h, it becomes a cube.
Key Components
Length (l) — the longest horizontal base measurement.
Width (w) — the shorter base measurement, perpendicular to length. Also called breadth.
Height (h) — the vertical dimension, perpendicular to both l and w.
Two Types of Rectangular Prism
Right rectangular prism: lateral faces perpendicular to the base. Standard everyday form.
Oblique rectangular prism: lateral faces not perpendicular. Height = perpendicular distance between bases.
The same formula V = l × w × h applies to both types.
Step-by-Step Calculation
Rectangle vs Rectangular Prism
A rectangle is a 2D flat shape with length and width; a rectangular prism is a 3D solid with length, width, and height. A rectangle has area but no volume. A rectangular prism has both volume and surface area.
| Property | Rectangle | Rectangular Prism |
|---|---|---|
| Dimensions | 2 (length, width) | 3 (length, width, height) |
| Shape type | 2D flat figure | 3D solid figure |
| Measurement | Area = l × w | Volume = l × w × h |
| Result units | Square (cm², in², m²) | Cubic (cm³, in³, m³) |
| Faces | 1 flat surface | 6 rectangular faces |
| Edges | 4 | 12 |
| Vertices | 4 | 8 |
A rectangle is one face of a rectangular prism. Every rectangular prism has 6 rectangular faces—each face is a rectangle. A rectangle cannot hold liquid, material, or enclosed space. A rectangular prism can.
Example: A sheet of paper (30 cm × 20 cm) is a rectangle. Its area = 30 × 20 = 600 cm². A ream of paper (30 cm × 20 cm × 5 cm) is a rectangular prism. Its volume = 30 × 20 × 5 = 3,000 cm³ (3 liters or approximately 183.1 in³).
Volume of a Rectangular Prism
The volume of a rectangular prism is the total 3D space enclosed within the solid, found by multiplying its length, width, and height.
Formula for a Rectangular Prism
Where:
• l = length
• w = width
• h = height
• V = volume in cubic units
An equivalent form: V = B × h, where B is the base area (l × w). Use this form when the base area is already known.
4 worked examples:
Example 1: A rectangular prism is 8 cm long, 5 cm wide, and 3 cm tall.
V = 8 × 5 × 3 = 120 cm³ (0.12 liters or approximately 7.32 in³)
Example 2: A rectangular prism is 2 ft long, 1.5 ft wide, and 1 ft tall.
V = 2 × 1.5 × 1 = 3 ft³ (approximately 84.95 liters or 22.44 US gallons)
Example 3: A rectangular prism is 10 m long, 4 m wide, and 2.5 m tall.
V = 10 × 4 × 2.5 = 100 m³ (100,000 liters or 26,417 US gallons)
Example 4: A rectangular prism is 12 in long, 9 in wide, and 6 in tall.
V = 12 × 9 × 6 = 648 in³ (approximately 10.61 liters or 2.8 US gallons)
Rectangle Volume in Litres
To calculate rectangle volume in litres, compute the volume in cubic centimeters (cm³) and divide by 1,000. One litre (L) equals exactly 1,000 cm³ (one cubic decimeter, dm³).
Conversion formula: Volume (L) = Volume (cm³) ÷ 1,000
Example 1: A rectangular box is 20 cm × 15 cm × 10 cm.
V = 20 × 15 × 10 = 3,000 cm³ ÷ 1,000 = 3 litres
Example 2: A rectangular tank is 50 cm × 30 cm × 40 cm.
V = 50 × 30 × 40 = 60,000 cm³ ÷ 1,000 = 60 litres
Example 3: A storage bin is 1 m × 0.5 m × 0.8 m.
V = 1 × 0.5 × 0.8 = 0.4 m³ × 1,000 = 400 litres
Conversion reference — rectangle volume to litres:
| Starting unit | Multiply by | To get litres |
|---|---|---|
| cm³ | ÷ 1,000 | L |
| m³ | × 1,000 | L |
| in³ | × 0.016387 | L |
| ft³ | × 28.3168 | L |
| US gallons | × 3.78541 | L |
Rectangle Volume to Gallons
To convert rectangle volume to US gallons, calculate the volume in cubic inches (in³) and divide by 231. For imperial (UK) gallons, divide by 277.42 instead.
US gallons formula: V (US gal) = V (in³) ÷ 231
Imperial gallons formula: V (imp gal) = V (in³) ÷ 277.42
From cubic centimeters:
• V (US gal) = V (cm³) × 0.000264172
• V (imp gal) = V (cm³) × 0.000219969
From cubic meters:
• V (US gal) = V (m³) × 264.172
• V (imp gal) = V (m³) × 219.969
Example 1 (US gallons from inches): A rectangular tank is 24 in × 12 in × 16 in.
V = 24 × 12 × 16 = 4,608 in³ ÷ 231 = 19.95 US gallons (approximately 75.5 liters)
Example 2 (US gallons from centimeters): A rectangular container is 60 cm × 30 cm × 40 cm.
V = 60 × 30 × 40 = 72,000 cm³ × 0.000264172 = 19.02 US gallons (72 liters)
Example 3 (imperial gallons): A rectangular pond is 100 cm × 60 cm × 50 cm.
V = 100 × 60 × 50 = 300,000 cm³ × 0.000219969 = 65.99 imperial gallons (300 liters)
Quick conversion reference:
| Volume | US Gallons | Imperial Gallons | Litres |
|---|---|---|---|
| 1 ft³ | 7.481 | 6.229 | 28.317 |
| 1 m³ | 264.172 | 219.969 | 1,000 |
| 1,000 cm³ | 0.264 | 0.220 | 1 |
| 1 in³ | 0.00433 | 0.00360 | 0.01639 |
Rectangle Volume in Cubic Feet
To find rectangle volume in cubic feet, measure all three dimensions in feet and multiply: V (ft³) = l (ft) × w (ft) × h (ft).
Convert to feet first when dimensions arrive in other units:
• Inches → feet: divide by 12
• Centimeters → feet: divide by 30.48
• Meters → feet: multiply by 3.28084
Example 1 (dimensions in feet): A rectangular room is 12 ft × 10 ft × 8 ft.
V = 12 × 10 × 8 = 960 ft³ (approximately 27.18 m³ or 27,180 liters)
Example 2 (converting from inches): A box is 36 in × 24 in × 18 in.
Convert: 36 ÷ 12 = 3 ft; 24 ÷ 12 = 2 ft; 18 ÷ 12 = 1.5 ft
V = 3 × 2 × 1.5 = 9 ft³ (approximately 254.9 liters or 67.3 US gallons)
Example 3 (converting from centimeters): A container is 90 cm × 60 cm × 45 cm.
Convert: 90 ÷ 30.48 ≈ 2.953 ft; 60 ÷ 30.48 ≈ 1.969 ft; 45 ÷ 30.48 ≈ 1.476 ft
V ≈ 2.953 × 1.969 × 1.476 ≈ 8.59 ft³ (approximately 243.2 liters)
Cubic feet conversion reference:
| From | To ft³ |
|---|---|
| 1 m³ | 35.3147 ft³ |
| 1 L (1,000 cm³) | 0.0353 ft³ |
| 1,728 in³ | 1 ft³ |
| 1 US gallon | 0.1337 ft³ |
Rectangle Volume in Cubic Meters
To find rectangle volume in cubic meters, measure all dimensions in meters and multiply: V (m³) = l (m) × w (m) × h (m).
Convert to meters first when dimensions are in other units:
• Centimeters → meters: divide by 100
• Millimeters → meters: divide by 1,000
• Inches → meters: multiply by 0.0254
• Feet → meters: multiply by 0.3048
Example 1 (dimensions in meters): A rectangular warehouse is 15 m × 8 m × 4 m.
V = 15 × 8 × 4 = 480 m³ (480,000 liters or approximately 126,800 US gallons)
Example 2 (converting from centimeters): A container is 150 cm × 80 cm × 60 cm.
Convert: 1.5 m × 0.8 m × 0.6 m
V = 1.5 × 0.8 × 0.6 = 0.72 m³ (720 liters or approximately 190.2 US gallons)
Example 3 (converting from inches): A box is 48 in × 36 in × 24 in.
Convert: 48 × 0.0254 = 1.2192 m; 36 × 0.0254 = 0.9144 m; 24 × 0.0254 = 0.6096 m
V = 1.2192 × 0.9144 × 0.6096 ≈ 0.679 m³ (679 liters or approximately 179.4 US gallons)
Cubic meters conversion reference:
| From | To m³ |
|---|---|
| 1 ft³ | 0.028317 m³ |
| 1 in³ | 0.0000164 m³ |
| 1 L | 0.001 m³ |
| 1 US gallon | 0.003785 m³ |
| 1 UK gallon | 0.004546 m³ |
Rectangle Volume from Area
To calculate rectangle volume from area, multiply the base area by the height: V = A × h, where A is the area of the base (l × w) and h is the perpendicular height of the solid.
This approach is used when the base area is already known from a floor plan, area calculator, or technical specification. It avoids recalculating length and width separately.
Example 1 (garden bed): A rectangular garden bed has a base area of 12 m² and a soil depth of 0.3 m (30 cm or approximately 11.8 in).
V = 12 × 0.3 = 3.6 m³ (3,600 liters or approximately 951 US gallons)
Example 2 (storage room): A rectangular storage unit has a floor area of 48 ft² and a ceiling height of 8 ft.
V = 48 × 8 = 384 ft³ (approximately 10.87 m³ or 10,873 liters)
Example 3 (concrete slab): A concrete slab has a surface area of 25 m² and a thickness of 0.15 m (15 cm or approximately 6 inches).
V = 25 × 0.15 = 3.75 m³ (3,750 liters or approximately 990.6 US gallons)
Volume from area also applies when thickness is the known dimension:
V = base area × thickness
A steel plate with an area of 0.5 m² and a thickness of 0.02 m (2 cm or approximately 0.79 inches):
V = 0.5 × 0.02 = 0.01 m³ (10 liters or approximately 2.64 US gallons)
Volume of a Rectangular Pyramid
The volume of a rectangular pyramid is one-third the product of its base length, base width, and height: V = (1/3) × l × w × h.
A rectangular pyramid has a rectangular base and 4 triangular faces that meet at a single apex (vertex). The rectangular pyramid differs from a rectangular prism in one key way: the prism extends uniformly from base to top; the pyramid tapers to a point.
Where:
• l = base length
• w = base width
• h = perpendicular height from base to apex
Prism vs pyramid volume comparison:
| Shape | Formula | Volume (same 6 × 4 × 9 m base/height) |
|---|---|---|
| Rectangular prism | l × w × h | 216 m³ |
| Rectangular pyramid | (1/3) × l × w × h | 72 m³ |
A rectangular pyramid holds exactly 1/3 the volume of a rectangular prism with the same base dimensions and height.
Example 1: A rectangular pyramid has a base of 6 m × 4 m and a height of 9 m.
V = (1/3) × 6 × 4 × 9 = (1/3) × 216 = 72 m³ (72,000 liters)
Example 2: A decorative pyramid has a base of 5 in × 5 in and a height of 8 in.
V = (1/3) × 5 × 5 × 8 = (1/3) × 200 = 66.67 in³ (approximately 1.09 liters or 0.29 US gallons)
Example 3: A sand pyramid has a rectangular base of 3 ft × 2 ft and a height of 4 ft.
V = (1/3) × 3 × 2 × 4 = (1/3) × 24 = 8 ft³ (approximately 226.5 liters or 59.8 US gallons)
The formula derives from the general pyramid volume formula V = (1/3) × B × h, where B is the base area. For a rectangular base, B = l × w, giving V = (1/3) × l × w × h.
Volume of a Cuboid
The volume of a cuboid is V = l × w × h. A cuboid is the same shape as a rectangular prism — both terms describe a 3D solid with 6 rectangular faces, 12 edges, and 8 vertices. "Cuboid" is the standard term in British English and international mathematics curricula; "rectangular prism" is more common in American English.
Key properties of a cuboid:
| Property | Value |
|---|---|
| Faces | 6 (all rectangles) |
| Edges | 12 |
| Vertices | 8 |
| Volume | V = l × w × h |
| Surface area | SA = 2(lw + lh + wh) |
A cube is a special case of a cuboid where all three dimensions are equal (l = w = h = s), giving V = s³ and SA = 6s².
Example 1: A cuboid brick is 20 cm × 10 cm × 6.5 cm (approximately 7.87 in × 3.94 in × 2.56 in).
V = 20 × 10 × 6.5 = 1,300 cm³ (1.3 liters or approximately 79.3 in³)
Example 2: A cuboid box is 0.5 m × 0.4 m × 0.3 m.
V = 0.5 × 0.4 × 0.3 = 0.06 m³ (60 liters or approximately 15.85 US gallons)
Example 3: A cuboid swimming pool is 10 m × 5 m × 1.8 m.
V = 10 × 5 × 1.8 = 90 m³ (90,000 liters or approximately 23,775 US gallons)
Example 4: A cuboid cereal box is 8 in × 3 in × 11 in.
V = 8 × 3 × 11 = 264 in³ (approximately 4.33 liters or 1.14 US gallons)
Volume of a Rectangular Container
The volume of a rectangular container is V = l × w × h, calculated using the inner dimensions to determine how much the container holds.
For capacity — the amount of liquid, soil, gravel, or material a container can hold — always use the inner (interior) dimensions, not the outer dimensions. The outer dimensions include wall thickness and produce a larger, incorrect capacity figure.
Rectangular containers include storage bins, crates, shipping boxes, troughs, fish tanks, and planters. Volume determines:
• Liquid capacity (liters, gallons)
• Material fill quantity (soil, concrete, gravel)
• Storage capacity (number of items, packing efficiency)
Example 1 (storage bin): A plastic bin has inner dimensions of 60 cm × 40 cm × 30 cm (approximately 23.6 in × 15.7 in × 11.8 in).
V = 60 × 40 × 30 = 72,000 cm³ = 72 liters (approximately 19.0 US gallons)
Example 2 (shipping crate): A rectangular wooden crate has inner dimensions of 2 m × 1.2 m × 1 m.
V = 2 × 1.2 × 1 = 2.4 m³ (2,400 liters or approximately 634 US gallons)
Example 3 (raised garden bed): A raised garden bed has inner dimensions of 2.4 m × 1.2 m × 0.4 m (approximately 8 ft × 4 ft × 16 in).
V = 2.4 × 1.2 × 0.4 = 1.152 m³ (1,152 liters or approximately 304.5 US gallons of potting soil)
Example 4 (aquarium): A rectangular aquarium has inner dimensions of 90 cm × 45 cm × 45 cm.
V = 90 × 45 × 45 = 182,250 cm³ = 182.25 liters (approximately 48.1 US gallons)
Containers with wall thickness: Use the hollow rectangle method to find usable inner volume:
V_inner = (L − 2t) × (W − 2t) × (H − t), where t is the wall thickness and H uses only one wall at the base.
Volume of a Rectangular Tank
The volume of a rectangular tank is V = l × w × h, using inner dimensions for liquid capacity, expressed in liters or gallons.
Rectangular tanks are used in water storage, aquaculture, chemical processing, fuel storage, and wastewater treatment. The same formula applies to all rectangular tanks regardless of size. The Rectangular Tank Volume Calculator automates this calculation and handles unit conversion.
Full tank examples:
Example 1: A rectangular water tank has inner dimensions of 2 m × 1.5 m × 1 m.
V = 2 × 1.5 × 1 = 3 m³ = 3,000 liters = approximately 792.5 US gallons
Example 2: A rectangular fuel tank is 36 in × 18 in × 12 in.
V = 36 × 18 × 12 = 7,776 in³ ÷ 231 = 33.66 US gallons (approximately 127.4 liters)
Example 3: A rectangular aquaculture tank is 300 cm × 150 cm × 80 cm.
V = 300 × 150 × 80 = 3,600,000 cm³ ÷ 1,000 = 3,600 liters (approximately 950.8 US gallons)
Partial fill calculation:
For a tank filled to a height f (not completely full), replace h with f:
V_partial = l × w × f
Example: A 2 m × 1.5 m × 1 m tank is filled to 0.7 m (70 cm or approximately 27.6 in).
V = 2 × 1.5 × 0.7 = 2.1 m³ (2,100 liters or approximately 554.8 US gallons)
Rectangular tank volume conversion reference:
| Volume (m³) | Litres | US Gallons | Imperial Gallons |
|---|---|---|---|
| 0.1 | 100 | 26.42 | 22.00 |
| 0.5 | 500 | 132.09 | 110.00 |
| 1.0 | 1,000 | 264.17 | 219.97 |
| 2.0 | 2,000 | 528.34 | 439.94 |
| 5.0 | 5,000 | 1,320.86 | 1,099.85 |
| 10.0 | 10,000 | 2,641.72 | 2,199.69 |
Volume of a Rectangular Box
The volume of a rectangular box is V = l × w × h, where l is the length, w is the width, and h is the height. A rectangular box is the everyday name for a rectangular prism (cuboid).
Volume determines how much a box can hold; surface area determines how much material is needed to make or wrap the box.
Surface area of a rectangular box:
SA = 2(lw + lh + wh)
Packaging and shipping use:
Shipping carriers calculate volumetric weight (dimensional weight) from rectangular box volume:
Volumetric weight = (l × w × h) ÷ 5,000
(where dimensions are in centimeters and the result is in kilograms, using the standard factor of 5,000 cm³/kg used by most major carriers)
Example 1 (small parcel): A box is 30 cm × 20 cm × 15 cm.
V = 30 × 20 × 15 = 9,000 cm³ (9 liters or approximately 2.38 US gallons)
Volumetric weight = 9,000 ÷ 5,000 = 1.8 kg
Surface area = 2(30 × 20) + 2(30 × 15) + 2(20 × 15) = 1,200 + 900 + 600 = 2,700 cm²
Example 2 (moving box): A box is 18 in × 18 in × 24 in (approximately 45.7 cm × 45.7 cm × 61 cm).
V = 18 × 18 × 24 = 7,776 in³ (approximately 127.4 liters or 33.67 US gallons)
Surface area = 2(18 × 18) + 2(18 × 24) + 2(18 × 24) = 648 + 864 + 864 = 2,376 in²
Example 3 (freight box): A box is 1.2 m × 0.8 m × 0.8 m.
V = 1.2 × 0.8 × 0.8 = 0.768 m³ (768 liters or approximately 202.9 US gallons)
Surface area = 2(1.2 × 0.8) + 2(1.2 × 0.8) + 2(0.8 × 0.8) = 1.92 + 1.92 + 1.28 = 5.12 m²
Volume vs surface area — rectangular box summary:
| Use case | Measurement needed | Formula |
|---|---|---|
| How much fits inside | Volume | l × w × h |
| How much wrapping paper | Surface area | 2(lw + lh + wh) |
| Shipping weight estimate | Volumetric weight | (l × w × h) ÷ 5,000 |
| Painting the outside | Surface area | 2(lw + lh + wh) |
Volume and Surface Area
A rectangular solid has two primary measurements used in geometry and construction: volume (3D space enclosed) and surface area (total area of all 6 outer faces).
Surface Area: SA = 2(lw + lh + wh)
The surface area adds the areas of the 3 pairs of opposite faces. Each pair is doubled because opposite faces are identical.
Volume and Surface Area of a Cube
A cube is a rectangular solid where l = w = h = s. All 6 faces are identical squares — a special case of the rectangular prism.
Cube Surface Area: SA = 6s²
Substituting equal dimensions into the rectangular solid formulas confirms these: V = s × s × s = s³ and SA = 2(s²) + 2(s²) + 2(s²) = 6s².
Common Mistakes and How to Avoid Them
There are 3 common mistakes when calculating the volume of a rectangle:
01 — Mixing Units
Use the same unit for all three dimensions. Combining meters with centimeters or inches with feet produces meaningless results. Convert all dimensions to the same unit first.
02 — Misreading Measurements
Double-check each dimension before calculating. Transposing length and width does not change the result (l × w = w × l), but misreading height directly changes the final volume. Verify carefully in digital rendering and architectural models.
03 — Forgetting Cubic Units
Volume is always in cubic units. Reporting volume in square units (cm², in²) is incorrect — those are surface area units. If you measure in centimeters, the answer is in cm³; in inches, in³.
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Frequently Asked Questions
The volume of a rectangular prism is the total three-dimensional space enclosed within the prism. It equals the product of the prism's length, width, and height, in cubic units. For example, 6 × 4 × 3 cm = 72 cm³ (≈ 0.072 L or 4.39 in³).
The formula is V = l × w × h. An equivalent expression is V = B × h, where B = l × w (base area). Both give the same result.
Four steps: (1) Record length with unit. (2) Record width in the same unit. (3) Record height in the same unit. (4) Multiply: V = l × w × h and express the result in cubic units.
Divide volume by base area: h = V ÷ (l × w). Example: V = 600 cm³, l = 10, w = 6 → h = 600 ÷ 60 = 10 cm. Same rearrangement works for any missing dimension.
The volume doubles. Vnew = l × w × (2h) = 2V. Doubling shelf height doubles usable container volume.
The volume stays the same. Vnew = (2l) × w × (h/2) = lwh = V. The doubling and halving cancel exactly.
Volume becomes 8 times larger: Vnew = 2l × 2w × 2h = 8V. Scaling all dimensions by k multiplies volume by k³ (2³ = 8, 3³ = 27).
Apply V = l × w × h directly to fractional values. Multiply numerators together and denominators together, then simplify.
Example: l = 8/5, w = 3/4, h = 2/3 → V = 48 ÷ 60 = 4/5 cubic units. Convert mixed fractions to improper first (1 3/5 = 8/5).
Use: V = (1/8) × √[(a²−b²+c²)(a²+b²−c²)(−a²+b²+c²)], where a, b, c are the diagonals of the three different rectangular faces. Derived by applying the Pythagorean theorem to each face diagonal to find the edge lengths, then multiplying them.