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Geometry

Capsule Calculator

Capsule volume & surface area. Free online Capsule Calculator. Calculate capsule online — fast, accurate, mobile-friendly, no signup needed.

Volume
395.840674
Surface area
301.592895

Derivation

  1. ├── 01Givenr = 3, h = 10
  2. ├── 02FormulaVolume: π × t² × a+4 / 3 × π × t² × t
  3. ├── 03Compute Volume395.840674
  4. ├── 04FormulaSurface area: 2 × π × t × a+4 × π × t²
  5. └── 05Compute Surface area301.592895
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§01What is

Understanding the Capsule Calculator

The Capsule Calculator computes Volume from 2 inputs: radius, cylinder length. Capsule volume & 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 Capsule Calculator sits in that toolkit — it capsule volume & 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+4 / 3 × π × t² × t | Surface area = 2 × π × t × a+4 × π × t²

Where

r
Radius
h
Cylinder length
Volume
Output value
Surface area
Output value
§03Practical Example

Step-by-step walkthrough

Scenario

Apply the formula to a realistic set of inputs: Radius = 3, Cylinder length = 10.

  1. 01Start by noting the input — Radius: 3.
  2. 02Start by noting the input — Cylinder length: 10.
  3. 03Substitute these values into the formula: Volume = π × t² × a+4 / 3 × π × t² × t | Surface area = 2 × π × t × a+4 × π × t²
  4. 04Compute Volume: the calculator returns 395.841.
  5. 05Compute Surface area: the calculator returns 301.593.
  6. 06Cross-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 Capsule 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: 395.841
  3. 03New Volume: 84.823
  4. 04Volume decreases by 78.6% → 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: 395.841
  3. 03New Volume: 2035.75
  4. 04Volume increases by 414.3% → use this sensitivity to plan for real-world variation.
03 · PATTERN

Cylinder length halved

h = 5 (from 10)

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

  1. 01New Cylinder length: 5
  2. 02Baseline Volume: 395.841
  3. 03New Volume: 254.469
  4. 04Volume decreases by 35.7% → use this sensitivity to plan for real-world variation.
04 · PATTERN

Cylinder length doubled

h = 20 (from 10)

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

  1. 01New Cylinder length: 20
  2. 02Baseline Volume: 395.841
  3. 03New Volume: 678.584
  4. 04Volume increases by 71.4% → 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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