Geometry Calculator
Compute area, perimeter, circumference, volume and surface area for 2D and 3D shapes — with the exact formula used shown for every answer.
Geometry Formulas Reference
This calculator uses the standard geometry formulas below. For circles and 3D shapes, π (pi) is taken as the precise value of Math.PI (≈ 3.14159265).
Area = πr² · Circumference = 2πr · Diameter = 2r
Area = ½ × base × height · Heron's: A = √(s(s−a)(s−b)(s−c)), s = (a+b+c)/2
Area = l × w · Perimeter = 2(l+w) · Diagonal = √(l²+w²)
Area = s² · Perimeter = 4s · Diagonal = s√2
Area = ½ × (a + b) × height
Area = base × height
Surface Area = 4πr² · Volume = (4/3)πr³
Volume = πr²h · Surface Area = 2πr(r + h)
Volume = s³ · Surface Area = 6s²
Frequently asked questions
How do you find the area of a circle?
The area of a circle is A = πr², where r is the radius (the distance from the centre to the edge). Square the radius and multiply by π (≈ 3.14159). For example, a circle with radius 5 has area π × 5² = π × 25 ≈ 78.54 square units. The circumference (perimeter) is 2πr.
How do you find the area of a triangle?
If you know the base and height, the area is A = ½ × base × height. If you only know the three side lengths a, b, c, use Heron's formula: first compute the semi-perimeter s = (a + b + c)/2, then A = √(s(s−a)(s−b)(s−c)). This calculator supports both methods — switch the input mode on the Triangle tab.
How do you find the perimeter of a rectangle?
The perimeter of a rectangle is P = 2(length + width) — add the length and width, then double the result. The area is length × width, and the diagonal (corner to corner) is √(length² + width²) by the Pythagorean theorem.
What is the difference between surface area and volume?
Surface area measures the total area of all the outer faces of a 3D shape (in square units), while volume measures how much space the shape encloses (in cubic units). For a sphere, surface area = 4πr² and volume = (4/3)πr³. For a cube of side s, surface area = 6s² and volume = s³.
How do you calculate the volume of a cylinder?
The volume of a cylinder is V = πr²h, where r is the base radius and h is the height. Essentially you find the area of the circular base (πr²) and multiply by the height. The total surface area, including both circular ends, is 2πr(r + h).