Updated August 2026

Roof Truss Angle Calculator

Roof angle, pitch and slope are three ways of saying the same thing, and every trade uses a different one. This calculator gives all three at once, plus the peak and heel cut angles and the slope factor that turns run into real rafter length.

Angle · Pitch · Slope
roof pitch to degrees
roof slope calculator
truss cut angle calculator

The basics

What is Roof Pitch and Angle?

Pitch is not only an aesthetic choice. It changes what roofing you can use, how much material you buy and how far the truss can span.

A steeper pitch gives the truss more depth at mid-span, which reduces chord forces and lets the same lumber span further. It also increases roof area, so sheathing and roofing both cost more.

Going the other way, every degree you lose costs you roofing options. Below 3:12 asphalt shingles (opens in a new tab) are out, and below roughly 2:12 most mechanically-seamed metal (opens in a new tab) is out too, leaving membrane systems that are detailed and priced differently.

Pitch (6:12) Rise in inches per 12 in of horizontal run. What framers and truss plants work in.
Angle (26.57°) The arctangent of rise over 12. What engineers, drawings and mitre saws use.
Slope % (50%) Rise over run times 100. Used in civil work and in most metric-country specifications.
Slope factor (1.1180) The multiplier that turns any horizontal distance into true length along the roof plane.

Measuring an existing roof

Hold a level horizontally against a rafter, mark 12 in along it, and measure straight up from that mark to the rafter's underside. That vertical measurement in inches is your pitch, and it works safely from inside the roof space.

The maths

Truss Angle Formula

Pitch, angle and slope conversions

Angle = arctan(Pitch ÷ 12)

Pitch = tan(Angle) × 12

Slope % = (Pitch ÷ 12) × 100

Slope factor = √(1 + (Pitch ÷ 12)²)

Heel cut = Angle

Peak cut = 90° - Angle

Multiply any horizontal distance by the slope factor to get the true length along the roof plane, including roof area from footprint.

Method

How to Calculate Roof Pitch and Angle

All three notations describe the same ratio, so converting between them is a single trigonometric step in each direction.

1 Set the pitch Use the preset chips or type an exact rise. The angle and slope percentage update instantly.
2 Read the cut angles The heel cut is the pitch angle itself and the peak cut is its complement. Together they always total 90 degrees.
3 Use the slope factor Multiply any horizontal distance by the slope factor to get the true length along the roof plane.
4 Check the roofing limits The tool flags pitches below the minimum for shingles, so you find out now rather than at inspection.

The confusion that costs money is between pitch and slope percentage. A 6:12 pitch is a 50% slope (opens in a new tab), not a 6% one, and specifying a roof at 6% slope when you meant 6:12 produces a roof that will not shed water at all.

On a mitre saw (opens in a new tab), remember that most saws are calibrated from square, so you may need to set the complement of the number you first think of. Cut an offcut and check it against the drawing before working through a stack of chords.

Worked example

At 6:12 the angle is 26.57 degrees, the slope is 50% and the slope factor is 1.1180. A 12 ft horizontal run becomes 13 ft 5 in of actual rafter, and a 1,000 ft² footprint becomes about 1,118 ft² of roof surface for ordering sheathing.

The complete conversion table for common roof pitches.

Roof Pitch to Angle Conversion
Pitch	Angle	Slope %	Slope factor	Suitable roofing
1:12	4.76°	8.3%	1.0035	Membrane only
2:12	9.46°	16.7%	1.0138	Metal with sealed laps
3:12	14.04°	25.0%	1.0308	Shingles at the minimum, double underlayment
4:12	18.43°	33.3%	1.0541	All standard roofing
5:12	22.62°	41.7%	1.0833	All standard roofing
6:12	26.57°	50.0%	1.1180	The most common residential pitch
8:12	33.69°	66.7%	1.2019	All roofing, roof jacks needed for access
10:12	39.81°	83.3%	1.3017	Steep, attic truss territory
12:12	45.00°	100.0%	1.4142	Steep, scaffolding required
16:12	53.13°	133.3%	1.6667	Very steep, near-vertical feel

Note: Minimum pitches for each roofing type are set by the manufacturer and by local code. Confirm both before finalising a low pitch.

The tool

Why Choose Our Truss Angle Calculator

Three trades use three different notations for the same slope, and this calculator shows all three at the same time.

Pitch, degrees and percent Enter any one and the other two follow, so nothing gets lost between drawings and the saw.
Both cut angles Heel and peak, which always total 90 degrees, ready to set on a mitre saw.
Slope factor given The multiplier that turns horizontal run into true rafter length and footprint into roof area.
Roofing limits flagged Pitches below the minimum for shingles are called out before they reach an inspector.

More tools

Calculators that pair with the angle & pitch tool, each running the same geometry engine.

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Answers

Frequently Asked Questions

Common questions about roof truss angle calculator.

How do I convert roof pitch to degrees?

Take the arctangent of the rise divided by 12. A 6:12 pitch is arctan(0.5), which is 26.57 degrees. The calculator converts in both directions, so you can enter either one.

What angle is a 4:12 roof pitch?

18.43 degrees, which is a 33.3% slope. It is the shallowest pitch most people would call a normal roof and it works with every standard roofing material.

What is the slope factor and why does it matter?

It is the square root of one plus the pitch over 12 squared, and it is the number you multiply a horizontal distance by to get the real distance along the slope. It converts building footprint into actual roof area for ordering sheathing and shingles.

What is the minimum roof pitch for shingles?

3:12 for standard asphalt shingle installation, and even then most manufacturers require a double layer of underlayment below 4:12. Below 3:12 you need a low-slope system such as membrane or mechanically-seamed metal.

What angle do I cut roof truss chords at?

The heel cut is the pitch angle and the peak cut is its complement, so at 6:12 that is 26.57 and 63.43 degrees. Most mitre saws are calibrated from square, so check an offcut before cutting a stack.

What is the most common roof pitch?

6:12 in North America. Steep enough to shed snow and water reliably, shallow enough to walk on with care, and well proportioned on a typical house. 4:12 is the most common on garages, sheds and outbuildings.

References

Pitch & Angle References

Related calculators on this site, plus the standards and reference works the figures on this page are based on. External links open in a new tab.

Authoritative external references

Codes and standards are revised on their own cycles. Confirm the current edition adopted in your jurisdiction with your local building department before relying on any figure.