Carpentry Math Basics

Feet-Inch-Fraction Arithmetic

Construction measurements are in feet, inches, and fractions — not decimals. You need to add 14' 3-1/2" + 8' 6-3/4"without converting to decimals first. Here's how:

The construction calculator handles this natively — enter values in feet-inch-fraction format and it does the arithmetic.

The Pythagorean Theorem (3-4-5)

a² + b² = c²— this one formula covers 80% of construction math. If you know two sides of a right triangle, you can find the third. It's how you calculate:

• Stair stringer length (rise² + run² = stringer²)
• Rafter length (rise² + run² = rafter²)
• Diagonal of a rectangle (for squaring)
• Any distance where you have horizontal and vertical measurements

The 3-4-5 rule is the practical application: if one side is 3, the other is 4, the diagonal is 5. Scale it up for squaring: 6-8-10, 9-12-15, 12-16-20. Snap a 3-foot line along one wall, a 4-foot line along the other, and if the diagonal measures exactly 5 feet, your corner is square.

Use the right triangle calculator for any rise/run/diagonal calculation.

Roof Pitch

Pitch is expressed as rise per 12 inches of run. A 6/12 pitch means the roof rises 6 inches for every 12 inches horizontally — that's a 26.6° angle. The pitch determines rafter length, roof area, and material quantities.

See the roof pitch chart for a complete conversion table from pitch to angle to slope factor.

Area and Volume

Construction area and volume come up constantly:

The concrete calculator handles cubic yard conversions. The board foot calculator handles lumber volume.

Common Conversions