Cubic Inches Calculator
Cubic Inches Calculator: How to Calculate Volume in Cubic Inches
Cubic inches (in³) measure the three-dimensional space inside a container, object, or shape. Whether you’re calculating shipping box dimensions for UPS or FedEx, figuring out an engine’s displacement, estimating how much mulch or concrete you need, or converting between units, the cubic inch calculator handles all of it. This guide covers the formula, conversions, and real-world applications.
What Is a Cubic Inch?
A cubic inch is the volume of a cube that measures exactly 1 inch on each side: 1 inch × 1 inch × 1 inch = 1 cubic inch (in³). It’s a unit of volume in the imperial and US customary systems, used across shipping, engineering, cooking, and construction.
The difference between an inch and a cubic inch:
An inch is a unit of length — it measures distance in one dimension. A cubic inch is a unit of volume — it measures space in three dimensions. You cannot compare them directly any more than you can compare metres to litres. One inch describes a line segment; one cubic inch describes a three-dimensional space.
Cubic Inches Formula
For any rectangular box or prism:
Volume (in³) = Length (in) × Width (in) × Height (in)
This is the core formula behind every cubic inches calculator. If your dimensions are in different units, convert them to inches first, then multiply.
Conversion Formula: Any Unit to Cubic Inches
If your length, width, and height are in feet:
Volume (in³) = L (ft) × W (ft) × H (ft) × 1,728
(since 1 ft = 12 in, and 12³ = 1,728)
If measurements are in centimetres:
Volume (in³) = L (cm) × W (cm) × H (cm) ÷ 16.387
If measurements are in metres:
Volume (in³) = L (m) × W (m) × H (m) × 61,023.74
How to Calculate Cubic Inches: Step by Step
Step 1 — Measure length, width, and height in inches using a tape measure or ruler
Step 2 — Multiply all three dimensions together
Volume = Length × Width × Height
Step 3 — The result is in cubic inches (in³)
Worked Example: Shipping Box
Box dimensions: 14 inches × 10 inches × 8 inches
Volume = 14 × 10 × 8 = 1,120 cubic inches
Worked Example: Starting from Feet
A container measures 3 feet × 2 feet × 1.5 feet. Convert to cubic inches:
3 × 2 × 1.5 = 9 cubic feet × 1,728 = 15,552 cubic inches
Volume Formulas by Shape
Not every object is a rectangular box. Here are cubic inch formulas for other common shapes:
| Shape | Formula | Variables |
|---|---|---|
| Rectangular box | V = L × W × H | Length, width, height |
| Cylinder | V = π × r² × h | r = radius, h = height |
| Sphere | V = (4/3) × π × r³ | r = radius |
| Cone | V = (1/3) × π × r² × h | r = radius, h = height |
| Cube | V = s³ | s = side length |
For a cylindrical can 4 inches in diameter and 6 inches tall:
r = 2 in V = π × 2² × 6 = 3.14159 × 4 × 6 = 75.4 cubic inches
Cubic Inches to Cubic Feet Conversion
The most common conversion needed in practice.
1 cubic foot = 12 × 12 × 12 = 1,728 cubic inches
| Direction | Formula |
|---|---|
| Cubic inches → Cubic feet | ÷ 1,728 |
| Cubic feet → Cubic inches | × 1,728 |
Cubic Feet to Cubic Inches Reference Table
| Cubic Feet | Cubic Inches |
|---|---|
| 0.5 cu ft | 864 in³ |
| 1 cu ft | 1,728 in³ |
| 1.5 cu ft | 2,592 in³ |
| 2 cu ft | 3,456 in³ |
| 3 cu ft | 5,184 in³ |
| 4 cu ft | 6,912 in³ |
| 5 cu ft | 8,640 in³ |
| 10 cu ft | 17,280 in³ |
| 12 cu ft | 20,736 in³ |
Is 12 cubic inches the same as 1 cubic foot? No. A common mistake is assuming 12 cubic inches = 1 cubic foot because 12 inches = 1 foot. But volume scales with the cube, not linearly. 1 cubic foot = 1,728 cubic inches (12³ = 1,728).
Cubic Inches to Cubic Yards
Useful for concrete and landscape material ordering.
1 cubic yard = 46,656 cubic inches (since 1 yd = 36 in, and 36³ = 46,656)
| Direction | Formula |
|---|---|
| Cubic inches → Cubic yards | ÷ 46,656 |
| Cubic yards → Cubic inches | × 46,656 |
For concrete or dirt estimates: if you know volume in cubic inches, divide by 46,656 to get cubic yards, then use that for ordering.
Cubic Inches to Cubic Meters (SI Conversion)
1 cubic inch = 0.000016387 cubic metres (m³)
1 cubic metre = 61,023.74 cubic inches
| Direction | Formula |
|---|---|
| Cubic inches → Cubic metres | × 0.000016387 |
| Cubic metres → Cubic inches | × 61,023.74 |
| Cubic Metres | Cubic Inches |
|---|---|
| 0.001 m³ (1 litre) | 61.02 in³ |
| 0.01 m³ | 610.2 in³ |
| 0.1 m³ | 6,102 in³ |
| 1 m³ | 61,024 in³ |
Complete Unit Conversion Reference
| From | To | Multiply By |
|---|---|---|
| Cubic inches (in³) | Cubic feet (ft³) | ÷ 1,728 |
| Cubic inches (in³) | Cubic yards (yd³) | ÷ 46,656 |
| Cubic inches (in³) | Cubic metres (m³) | × 0.000016387 |
| Cubic inches (in³) | Litres | × 0.016387 |
| Cubic inches (in³) | Millilitres | × 16.387 |
| Cubic inches (in³) | US fluid ounces | × 0.5541 |
| Cubic inches (in³) | US gallons | × 0.004329 |
| Cubic feet (ft³) | Cubic inches (in³) | × 1,728 |
| Cubic yards (yd³) | Cubic inches (in³) | × 46,656 |
| Litres | Cubic inches (in³) | × 61.024 |
| Centimetres (cm) → in³ | L(cm) × W(cm) × H(cm) | ÷ 16.387 |
Engine Cubic Inches Calculator
One of the most important uses of cubic inch calculation in engineering is engine displacement — the total volume swept by all pistons inside the cylinders.
Engine Cubic Inch Formula
Displacement (in³) = (π ÷ 4) × Bore² × Stroke × Number of Cylinders
Or equivalently:
Displacement (in³) = 0.7854 × Bore (in)² × Stroke (in) × Cylinders
Where bore = cylinder diameter, stroke = piston travel distance, both in inches.
Example: V8 engine, 4.00″ bore, 3.48″ stroke
0.7854 × 4.00² × 3.48 × 8 = 0.7854 × 16 × 3.48 × 8 = 350 cubic inches
Engine Displacement: Cubic Inches to Litres Chart
| Cubic Inches | Litres | Common Engines |
|---|---|---|
| 122 in³ | 2.0 L | 4-cylinder economy engines |
| 183 in³ | 3.0 L | V6 mid-size engines |
| 244 in³ | 4.0 L | Truck inline-6 |
| 305 in³ | 5.0 L | Small block V8 |
| 350 in³ | 5.7 L | Classic Chevy 350 |
| 383 in³ | 6.3 L | Stroker V8 |
| 427 in³ | 7.0 L | Big block V8 |
| 454 in³ | 7.4 L | Chevrolet big block |
| 502 in³ | 8.2 L | Performance big block |
Conversion formula: in³ × 0.016387 = litres | litres × 61.024 = in³
Cubic Inches for Shipping: UPS and FedEx Dimensional Weight
Carriers calculate shipping costs using dimensional weight (DIM weight), not just actual weight. DIM weight is based on cubic inches.
UPS Cubic Inches Calculator
DIM Weight (lbs) = L × W × H (in inches) ÷ DIM Factor
- UPS domestic DIM factor: 139
- FedEx domestic DIM factor: 139
- International shipments: typically 166
Example: Box measuring 18″ × 14″ × 10″:
Volume = 18 × 14 × 10 = 2,520 in³ DIM weight = 2,520 ÷ 139 = 18.1 lbs (round up to 19 lbs)
The carrier charges whichever is greater — actual weight or DIM weight. For large, lightweight items (pillows, foam, empty boxes), DIM weight almost always governs.
Cubic Inches for Mulch, Concrete, and Dirt
Landscaping and construction materials are sold by the cubic yard, but many calculations start in inches or feet. Here’s how to convert:
Volume (in³) to cubic yards:
Cubic yards = in³ ÷ 46,656
Volume from inches to cubic yards directly:
Cubic yards = (L” × W” × H”) ÷ 46,656
Coverage Tables
| Volume | Cubic Inches | Cubic Yards | Coverage at 3″ |
|---|---|---|---|
| 1 bag (2 cu ft mulch) | 3,456 in³ | 0.074 cu yd | ~8 sq ft |
| 1 cubic yard | 46,656 in³ | 1 cu yd | ~108 sq ft |
| 27 cubic feet | 46,656 in³ | 1 cu yd | ~108 sq ft |
Cubic Inches for Refrigerators and Appliances
When shopping for refrigerators, manufacturers list capacity in cubic feet. Convert to cubic inches to compare actual usable space:
Cubic feet × 1,728 = cubic inches
| Refrigerator Capacity | Cubic Inches |
|---|---|
| 10 cu ft (compact) | 17,280 in³ |
| 14 cu ft | 24,192 in³ |
| 18 cu ft (standard) | 31,104 in³ |
| 22 cu ft (large) | 38,016 in³ |
| 26 cu ft (XL) | 44,928 in³ |
Manufacturers measure internal volume including shelves and drawers, so the listed cubic feet is always approximate. Converting to cubic inches helps visualize the space when comparing models with the same listed capacity but different internal dimensions.
How to Calculate Cubic Inches for Irregular or Unusual Dimensions
Converting measurements in feet and inches (mixed units):
First, convert everything to decimal inches. Example: 2 feet 6 inches = (2 × 12) + 6 = 30 inches
Then multiply as normal.
Converting centimetres (cm) to cubic inches:
L(cm) × W(cm) × H(cm) ÷ 16.387 = cubic inches
From millimetres (mm):
L(mm) × W(mm) × H(mm) ÷ 16,387 = cubic inches
Price per cubic inch calculator:
Price per in³ = Total Price ÷ Volume in cubic inches
Useful for comparing material costs, packaging efficiency, or price per unit volume of products.
Frequently Asked Questions
How Do I Calculate Cubic Inches?
Measure the length, width, and height of the object or space in inches. Multiply all three together: Volume (in³) = Length × Width × Height. If your measurements are in feet, multiply by 1,728 to convert to cubic inches. If in centimetres, divide the L×W×H product by 16.387.
How Many Cubic Inches Are in a 12×12×12 Box?
A 12×12×12 inch box has a volume of 12 × 12 × 12 = 1,728 cubic inches. This is exactly 1 cubic foot, since 1 foot = 12 inches in each dimension.
How Many Cubic Inches Equal 1 Inch?
This question contains a unit mismatch — you cannot equate inches (a length) to cubic inches (a volume) any more than you can equate a line to a box. A single inch is one-dimensional; cubic inches are three-dimensional. One cubic inch equals exactly one inch in all three dimensions multiplied together (1 × 1 × 1 = 1 in³).
What Is 7.0 Litres in Cubic Inches?
7.0 litres × 61.024 = 427.2 cubic inches. This is why a 7.0-litre engine (like certain big-block V8s) is often called a “427” — it displaces approximately 427 cubic inches.
Is 12 Cubic Inches the Same as 1 Cubic Foot?
No. 1 cubic foot = 1,728 cubic inches. The confusion arises because 12 inches = 1 foot linearly, but volume scales with the cube: 12 × 12 × 12 = 1,728. Twelve cubic inches would be a box measuring 1″ × 1″ × 12″, or 2″ × 2″ × 3″ — nowhere near a cubic foot.
What’s the Difference Between an Inch and a Cubic Inch?
An inch measures length in one dimension — it tells you how long something is. A cubic inch measures volume in three dimensions — it tells you how much three-dimensional space something occupies. You need three length measurements (length, width, height) to get a volume in cubic inches. One is a line; the other is a box.