The Shape Calculator calculates the main measurements of common shapes: area and perimeter for 2D shapes (square, rectangle, triangle, circle) and volume and surface area for 3D shapes (cube, box, cylinder, sphere).
Each shape uses its standard formula — for example A = l × w for a rectangle, A = πr² for a circle, V = πr²h for a cylinder. Pick a shape and enter its dimensions in any unit. For irregular, composite or drawn shapes, use the specialized calculators listed below the tool.
Shape Calculator
Area, perimeter and volume of common 2D and 3D shapes — square, rectangle, triangle, circle, cube, box, cylinder and sphere.
Formula
2D shapes
| Shape | Area | Perimeter |
|---|---|---|
| Square | A = a² | P = 4a |
| Rectangle | A = l × w | P = 2(l + w) |
| Triangle (3 sides) | A = √(p(p − a)(p − b)(p − c)) | P = a + b + c |
| Circle | A = πr² | C = 2πr |
3D shapes
| Shape | Volume | Surface area |
|---|---|---|
| Cube | V = a³ | A = 6a² |
| Box | V = l × w × h | A = 2(lw + lh + wh) |
| Cylinder | V = πr²h | A = 2πr(r + h) |
| Sphere | V = (4/3)πr³ | A = 4πr² |
Where: a = side, l = length, w = width, h = height, r = radius, p = half the triangle’s perimeter.
How the Calculation Works
Step 1: Choose the shape. The calculator shows only the inputs that shape needs.
Step 2: Each dimension is converted to the same unit, so you can mix feet and inches or cm and m.
Step 3: The formulas above are applied and the results appear in square units (area) or cubic units (volume), which you can switch.
Variables Explained
| Measurement | What it describes | Unit |
|---|---|---|
| Perimeter | Distance around a flat shape | cm, m, in, ft |
| Area | Space inside a flat shape | cm², m², in², ft² |
| Surface area | Total area of a solid’s faces | cm², m², in², ft² |
| Volume | Space inside a solid | cm³, m³, L, ft³, gal |
Example Calculation
Rectangle
Given: 8 cm × 5 cm
Result: area = 40 cm², perimeter = 26 cm
Circle
Given: radius = 5 cm
Result: area = π × 25 ≈ 78.54 cm², circumference ≈ 31.42 cm
Cylinder
Given: radius = 3 cm, height = 10 cm
Result: volume = π × 9 × 10 ≈ 282.74 cm³, surface area ≈ 245.04 cm²
Common Conversion Table
| Unit | Equivalent |
|---|---|
| 1 m² | 10,000 cm² = 10.7639 ft² |
| 1 ft² | 144 in² |
| 1 m³ | 1,000 L |
| 1 ft³ | 1,728 in³ ≈ 7.48 US gal |
Shape Properties
2D vs 3D shapes
Flat (2D) shapes have length and width, so they have a perimeter and an area. Solid (3D) shapes add a third dimension, so they have a surface area and a volume.
Regular and irregular shapes
Regular shapes have equal sides and angles and simple formulas. Irregular shapes — such as a lot boundary or an odd-shaped room — need methods like coordinates, splitting into parts, or offsets, which the related calculators provide.
Dimensions Explained
Use the radius for circles, cylinders and spheres (half the diameter). For triangles, enter all three sides; if they cannot form a triangle, the calculator tells you.
Frequently Asked Questions
How do you calculate the area of a shape?
Use the formula for that shape: length × width for rectangles, πr² for circles, ½ × base × height for triangles. For irregular shapes, split them into simple shapes and add the areas.
What is the difference between area and perimeter?
Perimeter is the distance around the edge; area is the space inside.
What is the difference between volume and surface area?
Volume is the space inside a solid (cubic units); surface area is the total area of its outside (square units).
How do I find the area of an irregular shape?
Use the Irregular Shape Area Calculator, which works from corner coordinates, sides and a diagonal, offsets, or rectangles.
Can I mix units?
Yes. Choose a unit for each input and the calculator converts everything before calculating.
