Sphere Formulas Directory

A comprehensive index of 20 mathematical formulas, geometric proofs, and step-by-step guides for sphere dimensions.

V = 4/3 π r³

Sphere Volume Formula

Primary mathematical formula, historical Archimedes proof, and derivation.

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A = 4 π r²

Sphere Surface Area Formula

Formula for total outer boundary surface area and derivative link.

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V = 4/3 π r³

Formula for Volume of a Sphere

Step-by-step student guide to applying the volume formula.

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A = 4 π r²

Formula for Surface Area of a Sphere

How to calculate spherical surface area from radius or diameter.

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r = ³√[(3V)/(4π)]

Sphere Radius Formula

All inverse formulas to solve for radius from volume, area, or diameter.

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d = 2r

Sphere Diameter Formula

Relationships between diameter, radius, and spherical dimensions.

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C = 2 π r

Sphere Circumference Formula

Formula for calculating the perimeter of a sphere great circle.

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V = 4/3 π r³

Volume of Sphere Using Radius

How to use radius directly in volume calculations.

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V = 1/6 π d³

Volume of Sphere Using Diameter

Direct formula for volume when only diameter is given.

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A = 4 π r²

Surface Area of Sphere Using Radius

Standard surface area equation using radius.

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A = π d²

Surface Area of Sphere Using Diameter

Direct diameter formula for surface area calculation.

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4-Step Guide

How to Find Sphere Volume

Beginner-friendly tutorial on finding sphere volume.

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Step-by-Step

How to Find Sphere Surface Area

Complete guide to solving surface area problems.

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Inverse Roots

How to Find Radius of a Sphere

Rearranging volume and area formulas to isolate radius r.

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d = 2r

How to Find Diameter of a Sphere

Finding sphere diameter from volume, area, and circumference.

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V = 1/6 π d³

How to Find Sphere Volume From Diameter

Detailed walkthrough solving volume from diameter without errors.

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V = 4/3 π r³

How to Find Sphere Volume From Radius

Detailed walkthrough solving volume from radius.

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Full Working

How to Calculate Sphere Volume Step by Step

Step-by-step tutorial with algebraic working and visual checks.

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Quick Reference

Sphere Formula Cheat Sheet

Printable revision sheet containing all sphere formulas in one table.

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Middle & High School

Sphere Formulas for Students

Curriculum-aligned summary for exam revision and test preparation.

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