3D Shape Calculators
Free volume and surface area calculators for spheres, cylinders, cubes, and cones. All formulas shown with worked examples.
3D Shape Calculators - Volume and Surface Area for Every Solid
Three-dimensional geometry underpins engineering, architecture, manufacturing, and science. Whether you need concrete volume for a cylindrical column, storage capacity of a spherical tank, material for a cone-shaped hopper, or surface area of a cube for painting - these calculators give precise results with full formula breakdowns.
Four 3D Shape Calculators
Sphere Calculator - Enter radius to get volume (V = (4/3)πr³), surface area (A = 4πr²), and great-circle circumference. Works in reverse from volume or surface area to radius. Used for spherical tanks, medicine (tumour volume estimation), and astronomy.
Cylinder Calculator - Enter radius and height to get volume (V = πr²h), lateral surface area (A = 2πrh), total surface area including caps (A = 2πr(r+h)), and cross-section diagonal. Handles open-top cylinders. Combine with the Circle Calculator for the base area. Used for concrete columns, pipes, storage tanks, and food packaging.
Cube Calculator - Enter side length to get volume (s³), total surface area (6s²), face diagonal (s√2), and space diagonal (s√3). Works in reverse from volume. Used for storage box design, material estimation, and mathematical modelling.
Cone Calculator - Enter radius and height to get volume (V = (1/3)πr²h), slant height (l = √(r²+h²)), lateral surface area (A = πrl), total surface area including base, and base circumference. Used for funnel design, conical roofs, and industrial hoppers. Combine with the trig calculator for the apex half-angle.
Engineering Applications
Concrete volume - A cylindrical column 400 mm diameter × 3 m high: V = π × 0.2² × 3 = 0.377 m³. At ~₹6,000/m³ for M25 concrete (see the Concrete Mix Calculator), that is ₹2,260 per column. Tank capacity - A spherical water tank of radius 2.5 m holds 65,400 litres. Packaging - Surface area directly translates to material cost for any container shape.
Frequently Asked Questions
What is the formula for the volume of a sphere?
Volume = (4/3) × π × r³. For r = 5 cm: V = (4/3) × π × 125 = 523.6 cm³. Doubling the radius increases volume by 8× (volume scales with r³). Calculate it with the Sphere Calculator.
What is the difference between lateral and total surface area of a cylinder?
Lateral = the curved side only: 2πrh. Total = adds both end caps: 2πr(r+h). Use lateral for the body of a pipe; use total when including lids. Both are returned by the Cylinder Calculator.
How do I calculate the volume of a hollow cylinder?
V = π × h × (R² − r²), where R is the outer radius and r is the inner radius. Calculate each solid cylinder separately in the Cylinder Calculator and subtract.
What is the slant height of a cone and why does it matter?
Slant height l = √(r² + h²). It is used in the lateral surface area formula (πrl) and represents the actual slope length you measure along a conical roof or hopper. The Cone Calculator computes it automatically.