Roof Pitch Calculator

Every roof covering has a minimum pitch set by its manufacturer; check it against the pitch here.

Diagram
Pitch angle26.6°
Pitch50.0%
Rafter length with overhang3,913mm
Pitch
APitch angle26.6°
Pitch angle, to 0.01°26.57°
Pitch (rise ÷ run × 100)50.00 %
Ratio 1 : x (x = run ÷ rise)2.000
Rise per metre of run500 mm
Lengths
RRise1,500 mm
LRun3,000 mm
SSlope length over the run3,354 mm
Overhang length along the slope559 mm
Overhang drop (vertical)250 mm
TRafter (slope) length with overhang3,913 mm

About this calculator

This calculator converts a roof pitch between the three ways it is usually written — degrees, percent and a ratio 1 : x — from any two of pitch, rise and run. It also gives the slope length over the run and the full rafter length including a horizontal eaves overhang, with a dimensioned pitch triangle.

  • Rise — the vertical height the roof climbs.
  • Run — the horizontal distance it climbs over (for a symmetric gable roof, half the span).
  • Overhang — how far the eaves project past the wall line, measured horizontally.

It covers pitches from 0° to 75°.

Formula

pitch angle = atan(rise / run)
pitch %     = rise / run × 100
ratio 1 : x = 1 : (run / rise)
rise        = run × tan(angle) = run × % / 100 = run / x
run         = rise / tan(angle) = rise × 100 / % = rise × x

slope length       = √(rise² + run²) = run / cos(angle)
rafter with eaves  = (run + overhang) / cos(angle)
overhang drop      = overhang × tan(angle)

Worked example

A roof rising 1500 mm over a 3000 mm run, with a 500 mm overhang:

angle  = atan(1500 / 3000) = atan(0.5) = 26.57°
pitch  = 1500 / 3000 × 100 = 50 %;   ratio 1 : 2
slope  = √(1500² + 3000²) = 3354.1 mm
rafter = (3000 + 500) / cos 26.57° = 3913.1 mm

FAQ

What is the difference between degrees and percent? Percent is the rise per 100 units of run: 100% is 45°, not 90°. A 30° roof is 57.7%; a 10% roof is only 5.7°.

What does 1 : x mean? One unit of rise for every x units of run: 1 : 2 is 26.6°, 1 : 1 is 45°. It is common on drawings for low-pitched and flat roofs.

Which run do I enter for a gable roof? Half the span between the wall lines, for one slope. The rafter calculator also takes off the ridge board thickness and gives cut angles.

Which standard does this follow? None — this is trigonometry. The minimum pitch for a particular roof covering is set by the covering's manufacturer.

Assumptions and limits

  • One straight, plane slope; the rafter length is measured along the slope line (no ridge board deduction, no birdsmouth).
  • The overhang is entered horizontally and follows the same slope.
  • Percent and ratio inputs give exact results; an angle input is converted through its tangent once, so the last digit may be rounded.
  • Range 0–75°; at 0° the ratio is undefined and a rise cannot be reached.