Rectangular Tank / Box Volume Calculator
This calculator finds the volume, total surface area, and space diagonal of a rectangular prism (also known as a rectangular tank, box, or cuboid) based on its length, width, and height.
Enter the length (l), width (w), and height (h) below to calculate its properties. Ensure you use consistent units for all dimensions.
Enter Dimensions
Understanding Rectangular Volume & Formulas
What is a Rectangular Prism (Tank/Box)?
A rectangular prism, or cuboid, is a three-dimensional shape with six rectangular faces. All angles are right angles. It's a generalized form of a cube where the sides (length, width, height) can have different lengths. Common examples include boxes, rooms, aquariums, and bricks.
The Rectangular Volume Formula
The formula for rectangular volume (or the volume of a box) is found by multiplying its three dimensions: length (l), width (w), and height (h).
V = Length × Width × Height = l * w * h
Where:
- V is the Volume
- l is the length
- w is the width
- h is the height
This simple l*w*h formula calculates the 3D space inside the rectangular prism.
Other Rectangular Prism Formulas
- Total Surface Area (SA): The sum of the areas of the six rectangular faces (two of each: lw, lh, wh).
SA = 2 * (lw + lh + wh) - Space Diagonal (ds): The longest diagonal through the interior, from one corner to the opposite corner. Found using the Pythagorean theorem in 3D.
ds = √(l² + w² + h²)
Example Calculation (Provided in Original Text)
EX: Darby has a perfectly rectangular pack with length (l) = 4 ft, width (w) = 3 ft, and height (h) = 2 ft. Calculate the volume:
V = l * w * h = 4 ft * 3 ft * 2 ft = 24 cubic feet (ft³).
Real-Life Rectangular Volume Examples
Click on an example to see the step-by-step calculation:
Example 1: Shipping Box Volume
Scenario: Find the volume of a medium shipping box.
1. Known Values: Length (l) = 18 inches, Width (w) = 12 inches, Height (h) = 10 inches.
2. Formula: V = l * w * h
3. Calculation: V = 18 * 12 * 10
4. Result: V = 2160 cubic inches.
Conclusion: The box has a volume of 2160 cubic inches.
Example 2: Room Volume
Scenario: Calculate the volume of air in a small room (useful for HVAC calculations).
1. Known Values: Length (l) = 12 ft, Width (w) = 10 ft, Height (h) = 8 ft.
2. Formula: V = l * w * h
3. Calculation: V = 12 * 10 * 8
4. Result: V = 960 cubic feet.
Conclusion: The room has a volume of 960 cubic feet.
Example 3: Aquarium Volume
Scenario: Find the water capacity (volume) of a 20-gallon long aquarium tank.
1. Known Values: Length (l) = 30 inches, Width (w) = 12 inches, Height (h) = 12 inches.
2. Formula: V = l * w * h
3. Calculation: V = 30 * 12 * 12
4. Result: V = 4320 cubic inches. (Note: 1 US Gallon ≈ 231 cubic inches, so 4320 / 231 ≈ 18.7 gallons - close to the nominal 20 gal).
Conclusion: The aquarium holds approximately 4320 cubic inches of water.
Example 4: Dumpster Volume
Scenario: Estimate the volume of a small commercial dumpster.
1. Known Values: Approx. Length (l) = 6 ft, Width (w) = 4 ft, Height (h) = 4 ft.
2. Formula: V = l * w * h
3. Calculation: V = 6 * 4 * 4
4. Result: V = 96 cubic feet.
Conclusion: The dumpster has a capacity of roughly 96 cubic feet.
Example 5: Filing Cabinet Drawer Volume
Scenario: Calculate the internal storage volume of a standard letter-size filing cabinet drawer.
1. Known Values: Approx. Internal Length (l) = 25 in, Width (w) = 12 in, Height (h) = 10 in.
2. Formula: V = l * w * h
3. Calculation: V = 25 * 12 * 10
4. Result: V = 3000 cubic inches.
Conclusion: The drawer has an internal volume of 3000 cubic inches.
Example 6: Book Volume (Approximate)
Scenario: Estimate the volume occupied by a hardcover book.
1. Known Values: Approx. Length (l) = 9 inches, Width (w) = 6 inches, Height (h) = 1.5 inches.
2. Formula: V = l * w * h
3. Calculation: V = 9 * 6 * 1.5
4. Result: V = 81 cubic inches.
Conclusion: The book takes up about 81 cubic inches of space.
Example 7: Standard Brick Volume
Scenario: Find the volume of a standard US brick.
1. Known Values: Length (l) = 8 inches, Width (w) ≈ 3.625 inches, Height (h) = 2.25 inches.
2. Formula: V = l * w * h
3. Calculation: V = 8 * 3.625 * 2.25
4. Result: V = 65.25 cubic inches.
Conclusion: A standard brick has a volume of approximately 65.25 cubic inches.
Example 8: Microwave Oven Internal Volume
Scenario: Calculate the cooking capacity (internal volume) of a microwave.
1. Known Values: Approx. Internal Length (l) = 14 in, Width (w) = 13 in, Height (h) = 9 in.
2. Formula: V = l * w * h
3. Calculation: V = 14 * 13 * 9
4. Result: V = 1638 cubic inches (about 0.95 cubic feet).
Conclusion: The microwave has an internal cooking volume of about 1638 cubic inches.
Example 9: Swimming Pool Volume
Scenario: Estimate the volume of water needed to fill a rectangular swimming pool.
1. Known Values: Length (l) = 30 ft, Width (w) = 15 ft, Average Depth (h) = 5 ft.
2. Formula: V = l * w * h
3. Calculation: V = 30 * 15 * 5
4. Result: V = 2250 cubic feet (approx. 16,830 US gallons).
Conclusion: The pool holds about 2250 cubic feet of water.
Example 10: Plastic Storage Tote Volume
Scenario: Calculate the storage volume of a typical plastic tote box.
1. Known Values: Approx. Length (l) = 24 inches, Width (w) = 16 inches, Height (h) = 12 inches.
2. Formula: V = l * w * h
3. Calculation: V = 24 * 16 * 12
4. Result: V = 4608 cubic inches (approx. 2.67 cubic feet or 19.9 US gallons).
Conclusion: The storage tote has a volume of 4608 cubic inches.
Understanding Volume Measurement
Volume is the quantification of the three-dimensional space a substance occupies...
Common Volume Units Reference
Ensure your input length, width, and height use a consistent unit...
Frequently Asked Questions about Rectangular Volume
1. What is the formula for rectangular volume (volume of a box)?
The volume (V) is calculated by multiplying the length (l), width (w), and height (h): V = l * w * h.
2. What's the difference between a cube and a rectangular prism/tank?
A cube is a special type of rectangular prism where all edges (length, width, and height) are equal. A rectangular prism can have different values for length, width, and height.
3. How do I calculate the volume if I only know the area of the base and the height?
The area of the base of a rectangular prism is Base Area = length * width. So, the volume formula can also be written as V = Base Area * height.
4. What is the formula for the Total Surface Area of a rectangular prism?
The total surface area (SA) is the sum of the areas of all six rectangular faces: SA = 2*(lw + lh + wh).
5. What is the Space Diagonal and how is it calculated?
The space diagonal is the longest straight line inside the box, connecting opposite corners. It's calculated using the formula: ds = √(l² + w² + h²).
6. Does it matter which side I call length, width, or height?
No, for calculating volume and surface area, the order doesn't matter because multiplication is commutative (l*w*h = w*h*l, etc.). Just be consistent with your measurements.
7. What units should I use for length, width, and height?
Use any consistent unit of length (e.g., cm, inches, feet, meters). If you use inches for all three, the volume will be in cubic inches (in³), surface area in square inches (in²), and the diagonal in inches.
8. How can I find a missing dimension if I know the volume and the other two dimensions?
Rearrange the formula V = l * w * h. For example, if you know V, l, and w, you can find the height: h = V / (l * w).
9. Can I use this calculator for the volume of a room?
Yes, assuming the room is perfectly rectangular (ignoring alcoves, sloped ceilings etc.). Measure the internal length, width, and height to find the volume of air inside.
10. What is a cuboid?
Cuboid is another name for a rectangular prism.
11. How does volume change if I double only the length?
If you double the length (to 2l), the new volume becomes V = (2l) * w * h = 2 * (lwh). The volume doubles.
