Geometry Calculator
Twelve Shapes, One Reference
Every geometric shape has its own area, perimeter, volume, or surface-area formula, and keeping them all straight — especially the less common ones like a trapezoid's area or a cone's slant height — is exactly the kind of thing worth automating. This calculator covers rectangles, squares, circles, triangles, cubes, cuboids, spheres, cylinders, cones, trapezoids, ellipses, and regular polygons, applying the correct formula for whichever shape and measurement is selected.
The Formulas
Rectangle: Area = L × W, Perimeter = 2(L + W)
Square: Area = s², Perimeter = 4s
Circle: Area = πr², Circumference = 2πr
Triangle: Area = ½ × base × height, Perimeter = a + b + c
Cube: Volume = s³, Surface Area = 6s²
Cuboid: Volume = L × W × H, Surface Area = 2(LW + LH + WH)
Sphere: Volume = (4/3)πr³, Surface Area = 4πr²
Cylinder: Volume = πr²h, Surface Area = 2πr(r + h)
Cone: Volume = ⅓πr²h, Surface Area = πr(r + slant), slant = √(r² + h²)
Trapezoid: Area = ½(base1 + base2) × height
Ellipse: Area = πab (Ramanujan approximation used for perimeter)
Regular Polygon: Perimeter = n × side, Area = ns² ÷ (4 tan(π/n))
Square: Area = s², Perimeter = 4s
Circle: Area = πr², Circumference = 2πr
Triangle: Area = ½ × base × height, Perimeter = a + b + c
Cube: Volume = s³, Surface Area = 6s²
Cuboid: Volume = L × W × H, Surface Area = 2(LW + LH + WH)
Sphere: Volume = (4/3)πr³, Surface Area = 4πr²
Cylinder: Volume = πr²h, Surface Area = 2πr(r + h)
Cone: Volume = ⅓πr²h, Surface Area = πr(r + slant), slant = √(r² + h²)
Trapezoid: Area = ½(base1 + base2) × height
Ellipse: Area = πab (Ramanujan approximation used for perimeter)
Regular Polygon: Perimeter = n × side, Area = ns² ÷ (4 tan(π/n))
Where Each Shape Comes Up
- Home and construction projects — flooring (rectangle area), fencing (perimeter), or paint coverage.
- Packaging and shipping — cuboid volume for box capacity, cylinder volume for cans and tubes.
- Engineering and design — cone and sphere surface area for tanks, funnels, and pressure vessels.
- Classroom geometry — verifying area and perimeter answers across the full range of standard shapes.
| Shape | Dimensions | Measurement | Result |
|---|---|---|---|
| Rectangle | L=8, W=5 | Area | 40 |
| Circle | r=6 | Area | 113.097336 |
| Cube | s=4 | Volume | 64 |
| Sphere | r=3 | Volume | 113.097336 |
| Cylinder | r=3, h=10 | Volume | 282.743339 |
Circle and sphere areas above use π = 3.14159265…; values are rounded to six decimal places, matching the calculator's output precision.
How to Use This Calculator
- Select a shape from the dropdown — rectangle, square, circle, triangle, cube, cuboid, sphere, cylinder, cone, trapezoid, ellipse, or regular polygon.
- Choose the measurement to calculate (area, perimeter, volume, or surface area — options change based on the shape).
- Enter the required dimensions (length, width, radius, height, sides, and so on).
- Select Calculate to see the formula applied with your numbers and the final result.
Related Calculations
Working specifically with right triangles? The Pythagorean Theorem Calculator and Hypotenuse Calculator handle that case directly.