Area and Volume Calculator
Results
Show calculation steps and formula
How the calculator works
Select a shape, enter the required dimensions with their units, and optionally add a depth to turn an area into a volume. The calculator converts every input to meters using exact conversion factors, computes the result, then converts the result to your chosen output units. No intermediate rounding occurs — only the displayed values are rounded.
Supported shapes and formulas
| Shape | Area formula | Volume formula |
|---|---|---|
| Rectangle | length × width | Area × depth |
| Triangle | ½ × base × height | Area × depth |
| Circle | π × radius² | Area × depth |
| Trapezoid | ½ × (a + b) × height | Area × depth |
| Box | — | length × width × height |
| Cylinder | — | π × radius² × height |
| Sphere | — | ⁴⁄₃ × π × radius³ |
| Cone | — | ⅓ × π × radius² × height |
Exact conversion factors used
- 1 inch = 0.0254 meters (exact)
- 1 foot = 0.3048 meters (exact, international foot)
- 1 yard = 0.9144 meters (exact)
- 1 square foot = 0.09290304 square meters (exact)
- 1 cubic foot = 0.028316846592 cubic meters (exact)
- 1 cubic yard = 27 cubic feet (exact)
- 1 US gallon = 231 cubic inches = 3.785411784 liters (exact)
Worked examples
When to use each shape
✓ Included in this calculator
- Rectangle — rooms, slabs, walls, flooring
- Triangle — gable ends, roof sections, wedge spaces
- Circle — round tanks, columns, circular patios
- Trapezoid — sloped lots, tapered spaces
- Box — rooms, containers, shipping boxes, concrete footings
- Cylinder — tanks, pipes, posts, columns
- Sphere — spherical tanks, dome volumes
- Cone — hoppers, funnels, conical piles
✗ Not included
- Irregular land boundaries — use a surveyor or GIS tool
- Map-based area measurement — not a mapping calculator
- Cost estimation — see Concrete Calculator for materials cost
- Waste/overage factors — add your own percentage
- Legal property measurement — consult a licensed surveyor
Common mistakes and key conditions
- Mixing units without converting: Always use the unit selector per field; the calculator handles exact conversion.
- Feet-and-inches confusion: Enter feet and inches in separate fields or use the combined feet-inches input; 6 inches = 0.5 feet, not 0.6 feet.
- Radius vs diameter: Circle and cylinder inputs ask for radius. If you have diameter, divide by 2.
- Triangle height: The height must be perpendicular to the chosen base, not the side length.
- Trapezoid parallel sides: Sides a and b must be the parallel sides; height is the perpendicular distance between them.
- Depth vs height: For area shapes, "depth" creates a prism. For 3D shapes, the third dimension is called "height" in the formula.
- US gallon vs Imperial gallon: This calculator uses US gallons (231 cubic inches). Imperial gallons are larger (≈ 277.4 cubic inches).
Frequently asked questions
How do I calculate square feet for a rectangular room?
Select "Rectangle", enter the length and width in feet (or feet and inches), and the calculator returns the area in square feet, square yards, and square meters. The formula is length × width.
What is the difference between cubic feet and cubic yards?
1 cubic yard = 27 cubic feet (exactly). A cubic yard is a cube 3 feet on each side (3 ft × 3 ft × 3 ft = 27 cu ft). Materials like soil, mulch, and concrete are often sold by the cubic yard.
How do I convert cubic feet to US gallons?
1 US gallon = 231 cubic inches exactly. Since 1 cubic foot = 1,728 cubic inches, 1 cubic foot = 1,728 ÷ 231 ≈ 7.48052 US gallons. The calculator performs this exact conversion for cylinders, boxes, and any volume result.
Can I enter dimensions in feet and inches together?
Yes. Each dimension field has a unit selector. Choose "ft" for feet, "in" for inches, or enter the total in decimal feet (e.g., 12.5 for 12 ft 6 in). The calculator converts exactly using 1 inch = 0.0254 meters.
Does this calculator account for waste or overage?
No. The results are exact geometric calculations. For materials ordering, add your own waste factor (typically 5–10% for flooring, 10–15% for concrete).
What units does the calculator use internally?
All inputs are converted to meters using exact factors (1 ft = 0.3048 m, 1 in = 0.0254 m), computed in metric, then converted to your chosen output units. This avoids rounding errors from chaining conversions.
Is the US survey foot different from the international foot?
Yes. The US survey foot = 1200/3937 meters ≈ 0.3048006096 m. The international foot = 0.3048 m exactly. The US survey foot was deprecated in 2023. This calculator uses the international foot unless an official source specifies otherwise for a particular application.
Can I use this for legal property measurement?
No. This calculator assumes perfect geometric shapes and exact measurements. Legal property boundaries require a licensed land surveyor.
Glossary
- Square foot (sq ft)
- Unit of area equal to a square 1 foot on each side. 1 sq ft = 144 sq in = 0.09290304 m² exactly.
- Cubic foot (cu ft)
- Unit of volume equal to a cube 1 foot on each side. 1 cu ft = 1,728 cu in = 0.028316846592 m³ exactly.
- Cubic yard (cu yd)
- Unit of volume equal to a cube 1 yard (3 feet) on each side. 1 cu yd = 27 cu ft exactly.
- US gallon (gal)
- Unit of liquid volume. 1 US gal = 231 cu in = 3.785411784 L exactly. Not the same as an Imperial gallon.
- International foot
- The foot defined as exactly 0.3048 meters, adopted in 1959 and used throughout this calculator.
- Radius
- Distance from the center of a circle or sphere to its edge. Half the diameter.
- Trapezoid
- A quadrilateral with one pair of parallel sides (called bases a and b).
Official references
- NIST Office of Weights and Measures — https://www.nist.gov/pml/owm (Handbook 44, Appendix C for unit conversions)
- NIST — The International System of Units (SI) and US customary unit definitions
Conversion factors are exact definitions. No regulated rates or legal thresholds apply to this calculator.
Limitations, exclusions, and assumptions
- Perfect geometric shapes assumed; real-world objects may vary.
- User measurements are treated as exact; no measurement uncertainty is modeled.
- No waste, overage, compaction, or settling factors included.
- US gallon output for liquids is marked
ESTIMATE_WITH_LIMITATIONSuntil the gallon definition is verified against a primary NIST source. - Map-based land area, cost estimation, and legal property measurement are outside the scope of this calculator.
- The international foot (0.3048 m exactly) is used. The US survey foot differs slightly and was retired in 2023.
