# Carpentry Math

The carpentry math and formulas commonly used in nearly every carpentry project are listed below.

## How to calculate:

- Right Triangles
- Area of a Triangle
- Area of a Rectangle
- Volume of a Cube
- Area of a Trapezoid
- Circumference of a Circle
- Area of a Circle
- Volume of a Cylinder

## Carpentry Math - Right Triangles - The Pythagorean Theorem

The Pythagorean Theorem is used extensively in carpentry and construction. Almost every carpentry project involves some combination of squares and triangles.

The squared value of the hypotenuse of a right triangle is equal to the sum of the squared values of the other two sides. Essentially, side A squared plus side B squared equals side C squared.

A² + B² = C²

You can also calculate the length of an adjacent side by subtracting the hypotenuse squared minus either side squared. For example, side A squared equals side C squared minus side B squared.

A² = C² - B²

If this sounds complicated, consider the **3-4-5** rule of a right triangle. It is the best way to square two walls. Here's how it works - if one side of a right triangle is three feet and the adjacent side is four feet, the hypotenuse (or long side of the triangle) will be five feet, then angle 'A' is 90 degrees (see diagram at right). If you need to square walls in a large room, you can use proportions of this same formula, such as ** 6-8-10**.

5² = 4² + 3² or 10² = 8² + 6²

## How to Calculate the Area of a Triangle

The **A**rea of a triangle is equal to one-half the product of the **B**ase and **H**eight.

A = .5 x (B x H)

## How to Calculate the Area of a Rectangle

To calculate the **A**rea of a rectangle, multiply the **L**ength by the **W**idth.

A = L x W

## How to Calculate the Volume of a Cube

To calculate the **V**olume of a cube or box, multiply the **L**ength times the **W**idth times the **H**eight.

Volume = L x W x H

## How to Calculate the Area of a Trapezoid

To calculate the **A**rea of a trapezoid, multiply its **H**eight by one-half the sum of the parallel sides.

A = .5 x (L_{1} + L_{2}) x H

## How to Calculate the Circumference of a Circle

To calculate the **C**ircumference of a circle, multiply the **D**iameter times 3.1416 (pi).

C = 3.1416 x D

## How to Calculate the Area of a Circle

To calculate the **A**rea of a circle, multiply the **C**ircumference by one-half the **R**adius.

A = C x .5(R)

Or, multiply the radius squared by pi:

A = 3.1416 x R²

## How to Calculate the Volume of a Cylinder

To calculate the **V**olume of a cylinder, multiply the **R**adius squared x 3.1416 (pi) x the **H**eight of the cylinder.

V = 3.1416 x R² x H

**Carpentry Calculators** - Calculators used in carpentry.

**Framing Carpentry** - How to frame residential structures.

**Span Tables** - Calculate maximum rafter and joist spans.

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