Area & Volume Calculator
Calculate area and volume – rectangle, circle, triangle, cuboid, cylinder and sphere
Calculated in your browser – your inputs are not transmitted and are kept on this device only if you choose
Shape
Enter all measurements in the same unit – the result is in that unit squared (area) or cubed (volume), e.g. cm² or cm³.
Area (Rectangle)
20
20The area of the rectangle is 20 square units.
How this was calculated
RZ-26 · headon.pro
Calculate area: formulas for every shape
Circle area, rectangle and triangle – the most important area formulas
Calculating the area is one of the most common tasks in mathematics, trades and everyday life. The basic formula varies depending on the geometric shape: for a rectangle, the formula is A = a × b (length times width). When calculating a circle, the formula is A = π × r² – the so-called circle area formula, which squares the radius r and multiplies it by the constant π (≈ 3.14159). For a triangle, the formula is A = (g × h) / 2, i.e. base times height, halved.
The circle area is especially important in engineering and technology – for example when calculating pipe diameters, discs or round base areas. The radius is always half the distance from the center to the edge. If you only know the diameter d, then r = d ÷ 2. Our calculator shows the complete formula with the values inserted for every calculation, so you can follow the calculation step by step.
Calculate volume: cuboid, cylinder and sphere
Formulas and examples for the most important solids
Calculating the volume of geometric solids follows its own formula for each shape. A cuboid has the volume V = a × b × c (length × width × height). When calculating cylinder volume, the formula is V = π × r² × h – the circular base area multiplied by the height. The volume of a sphere is given by V = (4/3) × π × r³.
All three volume formulas build on area calculation: a cuboid's base is a rectangle (a × b), a cylinder's base is a circle (π × r²). For a cube, a = b = c, so V = a³. Cylinder volume is especially relevant in practice – for example for tanks, pipes and cans. Sphere volume is frequently needed in physics and chemistry, e.g. for molecule diameters or storage tanks.
- Formula
- A = π × r²
- Radius r
- 5 cm
- r²
- 25 cm²
- π × 25
- ≈ 78.54 cm²
- Circle area
- ≈ 78.54 cm²
- Formula
- V = π × r² × h
- Radius r
- 3 cm
- Height h
- 10 cm
- Base area π × 3²
- ≈ 28.274 cm²
- Volume 28.274 × 10
- ≈ 282.74 cm³
- Formula
- A = a × b
- Side a
- 6 m
- Side b
- 4 m
- Area
- 24 m²
Frequently asked questions about the Area & Volume Calculator
Formulas, examples and tips for geometry calculations
How do I calculate the area of a circle?
You calculate the area of a circle with the formula A = π × r², where r is the radius of the circle. For example, if a circle has a radius of 5 cm, the result is A = π × 5² ≈ 78.54 cm². If you know the diameter (d), then r = d ÷ 2. Our calculator performs the calculation instantly as soon as you enter the radius.
How do I calculate the volume of a cylinder?
You calculate cylinder volume with V = π × r² × h, where r is the radius of the base and h is the height of the cylinder. Example: radius 3 cm, height 10 cm → V = π × 9 × 10 ≈ 282.74 cm³. The base is a circle (π × r²), which multiplied by the height gives the volume.
How do I calculate the area of a rectangle?
You calculate the area of a rectangle with A = a × b, i.e. length times width. Example: a = 6 m, b = 4 m → A = 24 m². For a square, a = b, so A = a². The area of a rectangle is the simplest area calculation and forms the basis for many other geometric formulas.
What is the formula for the volume of a sphere?
You calculate the volume of a sphere with V = (4/3) × π × r³, where r is the radius of the sphere. Example: r = 4 cm → V = (4/3) × π × 64 ≈ 268.08 cm³. The formula shows that volume grows cubically with the radius – a sphere with twice the radius has eight times the volume.
How do I calculate the area of a triangle?
You calculate the area of a triangle with A = (g × h) / 2, i.e. base times height divided by 2. Example: g = 8 cm, h = 5 cm → A = (8 × 5) / 2 = 20 cm². The height must be perpendicular to the base. This relationship holds for every triangle – whether right-angled, isosceles or scalene.