Workshop Calculators - Real calculations for real work Workshop Calculators. Real calculations for real work.

Construction calculator

Roof Pitch Calculator

Translate roof rise and run into pitch, degrees, slope factor, and rafter length for layout and estimating.

Sage dressed as a carpenter
runriserafter

Enter the known values, choose the units or options, then calculate. Required or invalid entries will be identified before a result is shown.

Sage’s guided lesson

Let’s understand the result before using it

Calculate roof pitch, angle, rise per 12, slope factor, and rafter length from rise and run, with formulas and a worked example. I’ll show you what the numbers mean, how to check the math yourself, and where real-world conditions can change the answer.

Sage dressed as a teacher

Start with the real job

What this calculator is actually doing

Roof pitch compares vertical rise with horizontal run. In common U.S. notation, pitch is stated as inches of rise for 12 inches of run. The same right triangle also gives the roof angle and the sloped rafter length.

Sage’s rule

Rise and run must describe the same roof section. Use horizontal run, not the sloped rafter length.

Now for the arithmetic

How to do the math yourself

Pitch per 12 = rise ÷ run × 12. Angle = arctangent(rise ÷ run). Rafter length = square root of rise² + run².

Worked example

Rise = 6 in and run = 12 in.Pitch = 6 ÷ 12 × 12 = 6 in 12Angle = arctan(6 ÷ 12) ≈ 26.565°Rafter length over a 12 in run = √(12² + 6²) ≈ 13.416 in

Keep the angle and rafter length precise for layout, but report pitch in the conventional rise per 12 units when communicating with trades.

Sage dressed as a carpenter

I know this is off topic, but this reminds me of a joke I heard when teaching this to one of my interns, Why did the sock go to therapy? It had a hole in its heart. Yeah, I don’t see the connection either, but I think it is cute!

Sage dressed as a farmer

Before you cut, mix, or order

Tips, shortcuts, and mistakes to avoid

  • Use horizontal run, not the sloped roof surface, as the run input.
  • Half the building span is often the common rafter run, but overhang and ridge details must be handled separately.
  • Measure the existing roof in several places before assuming both sides or all sections match.
Do one reality check

Overhangs, ridge thickness, birdsmouth cuts, and real wall spacing must be added to the basic triangle separately.

How we got here

A little history and background

Builders described roof slope as a rise over a standard run long before electronic calculators. Framing squares include rafter tables that solve the same right triangle relationship for common pitches.

What the result does not tell you

The result is geometric only. It does not size rafters or include ridge reduction, heel height, birdsmouth, overhang, plumb cuts, structural loads, roofing requirements, or local code.

Sage dressed as a farmer

Frequently asked questions

What does a 6 in 12 pitch mean?

The roof rises 6 inches for every 12 inches of horizontal run.

Is roof pitch the same as roof angle?

They describe the same slope in different forms; pitch is a ratio and angle is measured in degrees.

Does the rafter length include the overhang?

Only if the run you enter includes the horizontal overhang.

That wraps up the lesson

Class is over. It is officially cheese fries time.

You now know more about how the Roof Pitch Calculator actually works, not just which buttons to press. That earns cheese fries, Sage’s favorite way to celebrate a finished lesson.

Sage dressed as a chef
Sage pointing while explaining something

Before you use the result

Verify the horizontal run, total rise, overhangs, ridge detail, and applicable structural requirements before cutting rafters.

Read the full disclaimer