Free Geometry Calculator with Steps
Calculate area, perimeter, volume, and surface area step-by-step. Learn geometry formulas with instant feedback. Perfect for GCSE and A-Level maths.
Step-by-step learning with explanations
Select Shape
Select a shape and enter dimensions, then click Calculate
Understanding Geometry Calculations
Geometry calculations help us understand the properties of shapes - their size, space, and dimensions. Area measures the 2D space inside a shape, while volume measures the 3D space inside a solid.
Perimeter is the total distance around a 2D shape, and surface area is the total area of all faces of a 3D shape. Understanding these concepts is essential for real-world applications in construction, design, and engineering.
2D Shape Formulas
Volume & Surface Area
Sphere & Cylinder
Sphere Volume: V = (4/3)πr³
Sphere Surface Area: SA = 4πr²
Cylinder Volume: V = πr²h
Cone & Pyramid
Cone Volume: V = (1/3)πr²h
Cone Surface Area: SA = πr² + πrl
Pyramid Volume: V = (1/3) × base × h
Prisms & Cuboids
Cuboid Volume: V = l × w × h
Cuboid Surface Area: SA = 2(lw + lh + wh)
Prism Volume: V = base area × height
How It Works
Select Shape
Choose from circles, triangles, rectangles, spheres, cylinders, and more.
Enter Dimensions
Input the measurements like radius, length, width, or height.
Choose Calculation
Select area, perimeter, volume, or surface area.
Learn or Get Answer
Learn Mode teaches each step; Quick Mode gives instant results.
Frequently Asked Questions
How do I calculate the area of a circle?
Use the formula A = πr². Square the radius and multiply by π (approximately 3.14159). For a radius of 5, area = π × 25 ≈ 78.54.
What is the formula for triangle area?
The standard formula is A = ½ × base × height. For right triangles, the two shorter sides can serve as base and height.
How do I calculate volume of a sphere?
Use V = (4/3)πr³. Cube the radius, multiply by π, then multiply by 4/3. A sphere with radius 3 has volume ≈ 113.1 cubic units.
What is the difference between area and perimeter?
Area measures the space inside a shape (in square units like cm²). Perimeter measures the distance around the outside (in linear units like cm).
How do I find the surface area of a cylinder?
Use SA = 2πr² + 2πrh. This combines two circular ends (2πr²) plus the curved side (2πrh, which "unrolls" to a rectangle).
Is this suitable for GCSE maths?
Yes! Covers all GCSE geometry topics including circles, triangles, rectangles, prisms, spheres, and cones with step-by-step working.
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