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Geometry

Rectangular Prism

Rectangular prism properties. Free online Rectangular Prism. Calculate rectangular prism online — fast, accurate, mobile-friendly, no signup needed.

Volume = l · w · h; surface area = 2(lw + lh + wh).
Volume
150
Surface area
190

Derivation

  1. ├── 01Givenl = 10, w = 5, h = 3
  2. ├── 02FormulaVolume: e.l × e.w × e.h
  3. ├── 03Substitutee.10 × e.5 × e.3
  4. ├── 04Compute Volume150
  5. ├── 05FormulaSurface area: 2 × (t × a+t × n+a × n)
  6. └── 06Compute Surface area190
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 Rectangular Prism

The Rectangular Prism computes Volume from 3 inputs: length, width, height. Rectangular prism properties.

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 Rectangular Prism sits in that toolkit — it rectangular prism properties. 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 = e.l × e.w × e.h | Surface area = 2 × (t × a+t × n+a × n)

Where

l
Length
w
Width
h
Height
Volume
Output value
Surface area
Output value
§03Practical Example

Step-by-step walkthrough

Scenario

Apply the formula to a realistic set of inputs: Length = 10, Width = 5, Height = 3.

  1. 01Start by noting the input — Length: 10.
  2. 02Start by noting the input — Width: 5.
  3. 03Start by noting the input — Height: 3.
  4. 04Substitute these values into the formula: Volume = e.l × e.w × e.h | Surface area = 2 × (t × a+t × n+a × n)
  5. 05Compute Volume: the calculator returns 150.
  6. 06Compute Surface area: the calculator returns 190.
  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 Rectangular Prism 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

Length halved

l = 5 (from 10)

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

  1. 01New Length: 5
  2. 02Baseline Volume: 150
  3. 03New Volume: 75
  4. 04Volume decreases by 50% → use this sensitivity to plan for real-world variation.
02 · PATTERN

Length doubled

l = 20 (from 10)

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

  1. 01New Length: 20
  2. 02Baseline Volume: 150
  3. 03New Volume: 300
  4. 04Volume increases by 100% → use this sensitivity to plan for real-world variation.
03 · PATTERN

Width halved

w = 2.5 (from 5)

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

  1. 01New Width: 2.5
  2. 02Baseline Volume: 150
  3. 03New Volume: 75
  4. 04Volume decreases by 50% → use this sensitivity to plan for real-world variation.
04 · PATTERN

Width doubled

w = 10 (from 5)

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

  1. 01New Width: 10
  2. 02Baseline Volume: 150
  3. 03New Volume: 300
  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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