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Geometry

Cone Volume Calculator

V = (1/3) π r² h. Free online Cone Volume Calculator. Calculate cone volume online — fast, accurate, mobile-friendly, no signup needed.

Volume = ⅓·π·r²·h.
Volume
47.12389

Derivation

  1. ├── 01Givenr = 3, h = 5
  2. ├── 02Formulaπ × t² × a / 3
  3. └── 03Compute Volume47.12389
Did you know?

The cone and pyramid share a single volume formula: V = (1/3) × base × height. Democritus (~450 BCE) asserted it; Eudoxus proved it a century later.

§01What is

Understanding the Cone Volume Calculator

The Cone Volume Calculator computes Volume from 2 inputs: radius, height. V = (1/3) π r² h.

Geometry is what turns raw measurements into useful answers about space — how much paint, how big a yard, how much material a project will need. Every craftsperson, architect, and DIYer reaches for these formulas regularly. The Cone Volume Calculator sits in that toolkit — it V = (1/3) π r² h. Enter your numbers above and the result updates instantly; every step of the math is shown in the Derivation panel so you can see exactly how the answer was reached.

§02The Formula

How it’s calculated

π × t² × a / 3

Where

r
Radius
h
Height
§03Practical Example

Step-by-step walkthrough

Scenario

Apply the formula to a realistic set of inputs: Radius = 3, Height = 5.

  1. 01Start by noting the input — Radius: 3.
  2. 02Start by noting the input — Height: 5.
  3. 03Substitute these values into the formula: π × t² × a / 3
  4. 04Compute Volume: the calculator returns 47.1239.
  5. 05Cross-check the answer by opening the Derivation panel above — every line of math is shown so you can follow the computation end-to-end.
§04Variants

Common Cone Volume Problems

The formula gets rearranged depending on which variable you need. Here are the patterns you’ll run into in the real world — find the one that matches your problem and follow the worked steps.

01 · PATTERN

Radius halved

r = 1.5 (from 3)

Keep every other input at its default and halve the radius. See how volume responds.

  1. 01New Radius: 1.5
  2. 02Baseline Volume: 47.1239
  3. 03New Volume: 11.781
  4. 04Volume decreases by 75% → use this sensitivity to plan for real-world variation.
02 · PATTERN

Radius doubled

r = 6 (from 3)

Keep every other input at its default and double the radius. See how volume responds.

  1. 01New Radius: 6
  2. 02Baseline Volume: 47.1239
  3. 03New Volume: 188.496
  4. 04Volume increases by 300% → use this sensitivity to plan for real-world variation.
03 · PATTERN

Height halved

h = 2.5 (from 5)

Keep every other input at its default and halve the height. See how volume responds.

  1. 01New Height: 2.5
  2. 02Baseline Volume: 47.1239
  3. 03New Volume: 23.5619
  4. 04Volume decreases by 50% → use this sensitivity to plan for real-world variation.
04 · PATTERN

Height doubled

h = 10 (from 5)

Keep every other input at its default and double the height. See how volume responds.

  1. 01New Height: 10
  2. 02Baseline Volume: 47.1239
  3. 03New Volume: 94.2478
  4. 04Volume increases by 100% → use this sensitivity to plan for real-world variation.
§05FAQ

Frequently asked questions

Yes. The calculator implements the standard formula as documented and returns exact floating-point results. No approximations are used unless noted in the formula.
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