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Geometry

Cone Calculator

Cone volume and surface area. Free online Cone Calculator. Calculate cone online — fast, accurate, mobile-friendly, no signup needed.

Volume = ⅓·π·r²·h; slant ℓ = √(r² + h²).
Volume
314.159265
Slant height
13
Surface area
282.743339

Derivation

  1. ├── 01Givenr = 5, h = 12
  2. ├── 02FormulaVolume: π × t² × a / 3
  3. ├── 03Compute Volume314.159265
  4. ├── 04FormulaSlant height: √(t²+a²)
  5. ├── 05Compute Slant height13
  6. ├── 06FormulaSurface area: π × t × (t+√(t²+a²))
  7. └── 07Compute Surface area282.743339
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 Calculator

The Cone Calculator computes Volume from 2 inputs: radius, height. Cone volume and surface area.

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 Calculator sits in that toolkit — it cone volume and surface area. 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

Volume = π × t² × a / 3 | Slant height = √(t²+a²) | Surface area = π × t × (t+√(t²+a²))

Where

r
Radius
h
Height
Volume
Output value
Slant height
Output value
Surface area
Output value
§03Practical Example

Step-by-step walkthrough

Scenario

Apply the formula to a realistic set of inputs: Radius = 5, Height = 12.

  1. 01Start by noting the input — Radius: 5.
  2. 02Start by noting the input — Height: 12.
  3. 03Substitute these values into the formula: Volume = π × t² × a / 3 | Slant height = √(t²+a²) | Surface area = π × t × (t+√(t²+a²))
  4. 04Compute Volume: the calculator returns 314.159.
  5. 05Compute Slant height: the calculator returns 13.
  6. 06Compute Surface area: the calculator returns 282.743.
  7. 07Cross-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 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 = 2.5 (from 5)

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

  1. 01New Radius: 2.5
  2. 02Baseline Volume: 314.159
  3. 03New Volume: 78.5398
  4. 04Volume decreases by 75% → use this sensitivity to plan for real-world variation.
02 · PATTERN

Radius doubled

r = 10 (from 5)

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

  1. 01New Radius: 10
  2. 02Baseline Volume: 314.159
  3. 03New Volume: 1256.64
  4. 04Volume increases by 300% → use this sensitivity to plan for real-world variation.
03 · PATTERN

Height halved

h = 6 (from 12)

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

  1. 01New Height: 6
  2. 02Baseline Volume: 314.159
  3. 03New Volume: 157.08
  4. 04Volume decreases by 50% → use this sensitivity to plan for real-world variation.
04 · PATTERN

Height doubled

h = 24 (from 12)

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

  1. 01New Height: 24
  2. 02Baseline Volume: 314.159
  3. 03New Volume: 628.319
  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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