MetreMate

Free calculator

Roof pitch calculator

Pitch in degrees = atan(rise ÷ run). A 1660 mm rise over 4000 mm is 22.5°, or about 1 in 2.4. Rafter length = run ÷ cos(pitch): 4 m of run at 22.5° is a 4.33 m rafter.

Your job

What do you know?

Rise is the height gained over the run, measured level (not along the slope).

Lengths

On a gable or hip roof this is half the building's width.

Steep enough for

  • Suits:Corrugated metal roofing (min 5°, 1 in 12)
  • Suits:Wide trapezoidal rib metal roofing (min 2°, 1 in 30)
  • Suits:Narrow rib metal roofing (min 3°, 1 in 20)
  • Suits:Concealed fix metal roofing (min 2°, 1 in 30)

Minimums for 0.42 mm sheet from the maker's manual. Tiles and other roofing have their own minimums.

5° min2° min3° min22.5°Run 4.00 mRise 1.66 mRafter 4.331 m1 in 2.4 · 41.5% grade · 415 mm rise per metre

The roof triangle to scale. Dashed lines mark each metal profile's minimum pitch.

Pitch

22.5°

1 in 2.4, 415 mm rise per metre

As a ratio

2.4(1 in N)

41.5% grade

Rafter factor

1.083

Slope length ÷ plan length

Hip and valley factor

1.474

Per metre of plan run

Rafter length

4.331m

For 4.00 m of plan run

Hip or valley

5.895m

Same run, equal-pitch hip roof

The working, with your numbers

  1. 1. Pitchatan(1,660 ÷ 4,000)= 22.54°
  2. 2. Rafter factor1 ÷ cos 22.54°= 1.083
  3. 3. Hip factor√(2 + tan² 22.54°)= 1.474
  4. 4. Rafter4.00 × 1.083= 4.331 m
Typed those measurements in by hand?MetreMate measures them straight off your PDF plans. Free to start.

The formula, in plain words

  1. 1Pitch (degrees) = atan(rise ÷ run). As a ratio, 1 in N where N = run ÷ rise. Grade % = rise ÷ run × 100.
  2. 2Rafter factor = 1 ÷ cos(pitch): slope length per metre of plan.
  3. 3Hip and valley factor = √(2 + tan² pitch), per metre of plan run on an equal-pitch hip roof.
  4. 4Rafter length = plan run × rafter factor. Hip length = plan run × hip factor.

Worked example

A roof that rises 1660 mm over a 4000 mm run (half an 8 m building).

  1. 1.Pitch: atan(1660 ÷ 4000) = 22.5°, or 1 in 2.4, a 41.5% grade.
  2. 2.Rafter factor: 1 ÷ cos 22.5° = 1.082. Rafter: 4 × 1.082 = 4.33 m.
  3. 3.Hip factor: √(2 + tan² 22.5°) = 1.474. Hip: 4 × 1.474 = 5.90 m.

Answer: 22.5°, a 4.33 m rafter and a 5.90 m hip.

How to measure it

  • Read the pitch off the elevations or truss drawings, or measure rise and run.
  • Rise is the height gained; run is the level distance, not along the slope.
  • For rafter lengths, the plan run is eaves to ridge: half the width on a gable or hip roof.
  • Measure on site before ordering roof sheets.

Where the numbers come from

Every default in the calculator is a number a supplier or manufacturer publishes. We list the source next to it so you can check.

WhatValueSource
Roof pitch factor (slope length ÷ plan length) = 1 ÷ cos(pitch); 25° gives 1.1031.103 at 25°Metroll, A Guide for Roofers (Met-TECH, 2023) (checked 2026-10-01)
Hip and valley factor = √(2 + tan² pitch) per metre of plan run; 25° gives 1.4891.489 at 25°Metroll, A Guide for Roofers (Met-TECH, 2023) (checked 2026-10-01)
Corrugated: minimum roof pitch 5° (1 in 12)5 ° minimumLysaght Roofing & Walling Installation Manual (2025) (checked 2026-10-01)
Wide trapezoidal rib: minimum pitch 2° (1 in 30)2 ° minimumLysaght Roofing & Walling Installation Manual (2025) (checked 2026-10-01)
Narrow rib: minimum pitch 3° (1 in 20)3 ° minimumLysaght Roofing & Walling Installation Manual (2025) (checked 2026-10-01)
Concealed fix: minimum pitch 2° (1 in 30) at 0.42 mm, 1° (1 in 50) at 0.48 mm2 ° minimumLysaght Roofing & Walling Installation Manual (2025) (checked 2026-10-01)

Manufacturers named here are the source of the number, not a recommendation. Confirm quantities with your supplier.

Frequently asked questions

Stop typing measurements in by hand

MetreMate measures every wall, floor and roof straight off your PDF plan. Then it hands you the same numbers this calculator asks for.

Try MetreMate free