Area measures how much surface a two-dimensional shape covers. Volume measures how much space a three-dimensional object occupies. These calculations are essential for painting a room, pouring concrete, buying carpet, sizing a water tank, shipping products, and hundreds of other practical tasks. This guide covers every common shape with clear formulas and real-world examples.
| Shape | Formula | Example |
|---|---|---|
| Rectangle | A = length × width | 12 ft × 10 ft = 120 sq ft |
| Square | A = side² | 8 ft × 8 ft = 64 sq ft |
| Triangle | A = ½ × base × height | ½ × 10 × 6 = 30 sq ft |
| Circle | A = π × r² | π × 5² = 78.5 sq ft |
| Trapezoid | A = ½(b1 + b2) × h | ½(8 + 12) × 5 = 50 sq ft |
| Parallelogram | A = base × height | 9 × 7 = 63 sq ft |
| Ellipse | A = π × a × b | π × 6 × 4 = 75.4 sq ft |
Use the Area Calculator to compute area for any shape, or the Circle Area Calculator for circular measurements.
Practical tip: For irregular rooms, break the space into rectangles and triangles, calculate each piece separately, and add them together. An L-shaped room is just two rectangles. A room with a bay window is a rectangle plus a trapezoid or triangle.
| Shape | Volume Formula | Surface Area Formula |
|---|---|---|
| Rectangular Box | V = l × w × h | SA = 2(lw + lh + wh) |
| Cube | V = s³ | SA = 6s² |
| Cylinder | V = πr²h | SA = 2πr(r + h) |
| Sphere | V = (4/3)πr³ | SA = 4πr² |
| Cone | V = (1/3)πr²h | SA = πr(r + √(r² + h²)) |
| Pyramid | V = (1/3) × base area × h | Base + lateral faces |
The Surface Area Calculator handles all of these shapes and more.
To calculate paint needed, find the total wall area: measure each wall’s width and height, multiply, and sum. A 12 × 14 foot room with 8-foot ceilings has wall area = 2(12 × 8) + 2(14 × 8) = 192 + 224 = 416 square feet. Subtract windows and doors (a standard door is about 21 sq ft, a window about 15 sq ft). One gallon of paint covers approximately 350–400 square feet, so this room needs about 1 gallon for one coat, 2 gallons for two coats.
Measure the room’s length and width in feet and multiply for square footage. Always add 10% for waste (cuts, mistakes, future repairs). A 15 × 20 foot room = 300 sq ft × 1.10 = 330 sq ft of material to purchase. For tile, divide total square footage by the area of one tile to find the count: 330 sq ft ÷ 1 sq ft per tile = 330 tiles.
Mulch, topsoil, and gravel are sold by the cubic yard. A flower bed 20 feet long, 4 feet wide, with 3 inches (0.25 feet) of mulch needs: 20 × 4 × 0.25 = 20 cubic feet ÷ 27 = 0.74 cubic yards. Rounding up to 1 cubic yard ensures you have enough.
Concrete is ordered in cubic yards. A 10 × 20 foot patio at 4 inches (0.333 feet) thick needs: 10 × 20 × 0.333 = 66.7 cubic feet ÷ 27 = 2.47 cubic yards. Order 2.75 or 3 cubic yards to account for waste and slight variations in thickness. At roughly $150–$170 per cubic yard delivered, this is a $370–$510 material cost.
A cylindrical water tank 4 feet in diameter and 6 feet tall holds: V = π × 2² × 6 = 75.4 cubic feet. Since 1 cubic foot = 7.48 gallons, the tank holds 75.4 × 7.48 = 564 gallons. A rectangular swimming pool 30 × 15 feet with an average depth of 5 feet holds: 30 × 15 × 5 = 2,250 cubic feet = 16,830 gallons.
Shipping costs are often based on dimensional weight: (L × W × H) ÷ a dimensional factor (typically 139 for domestic or 166 for international, in inches). A box 24 × 18 × 12 inches has dimensional weight = 5,184 ÷ 139 = 37.3 pounds. If the actual weight is 15 pounds, you pay for 37.3 pounds. This is why compact packaging saves money — reducing any dimension reduces the dimensional weight proportionally.
| Conversion | Factor |
|---|---|
| 1 square yard | 9 square feet |
| 1 acre | 43,560 square feet |
| 1 square meter | 10.764 square feet |
| 1 cubic yard | 27 cubic feet |
| 1 cubic foot | 7.481 gallons |
| 1 cubic meter | 264.2 gallons |
Confusing linear, square, and cubic units. A room that is 10 feet long has 10 linear feet of wall. If it is 10 × 10, it has 100 square feet of floor. If the ceiling is 10 feet high, it has 1,000 cubic feet of volume. Each dimension you multiply adds a power to the unit.
Forgetting to convert all measurements to the same unit. If length is in feet and width is in inches, convert one before multiplying. Mixing feet and inches is the most common source of area calculation errors.
Using diameter instead of radius. Circle and sphere formulas use radius (half the diameter). A 10-foot diameter circle has r = 5, so A = π × 25 = 78.5 sq ft, not π × 100 = 314 sq ft.
Calculate area and volume instantly. Use the free Area Calculator for 2D shapes, the Surface Area Calculator for 3D objects, and the Circle Area Calculator for circular measurements — no signup required.
Related tools: Area Calculator · Surface Area Calculator · Circle Area Calculator · Triangle Calculator · Circle Calculator · Square Footage Calculator