Unequal Pitch Roof Trigonometry
Calculating unequal pitched roofs is easy if you know what trigonometry functions to use. The
formulas below use the law of sines to calculate the unknown length or angle.


Known Variables: Major Pitch Angle & Minor Pitch Angle & Span & Plate Line Difference
Calculate Major & Minor Runs & Theoretical Plate Line Span
Theoretical Span = Span - (Plate Line Difference ÷ tan(Minor Pitch Angle))
Plate Line Difference Run = Span - Theoretical Span
Major Run = ((Theoretical Span × sin(Minor Pitch Angle)) ÷ sin (180 - Major Pitch Angle - Minor Pitch Angle)) × cos( Major Pitch Angle )
Theoretical Minor Run = ((Theoretical Span * sin(Major Pitch Angle)) ÷ sin (180 - Major Pitch Angle - Minor Pitch Angle)) × cos( Minor
Pitch Angle )
Minor Run = Theoretical Minor Run + Plate Line Difference Run
Major Rafter = Major Run ÷ cos (Major Pitch Angle)
Theoretical Minor Rafter = Theoretical Minor Run ÷ cos (Minor Pitch Angle)
Plate Line Difference Minor Rafter = Plate Line Difference Run ÷ cos (Minor Pitch Angle)
Minor Rafter = Minor Run ÷ cos (Minor Pitch Angle)
Roof Rise = Major Run × tan (Major Pitch Angle)
Total Minor Roof Rise = Minor Run × tan (Minor Pitch Angle)

Law Of Sines
C = 180° - (A + B)
a = ( c × sin( A) ) ÷ sin( C)
a = ( b × sin( A ) ) ÷ sin( B)
a = ( b ÷ sin( B ) ) × sin( A)
b = ( c × sin( B ) ) ÷ sin( C)
b = ( a × sin( B ) ) ÷ sin( A)
b = ( a ÷ sin( A ) ) × sin( B)
h = b × sin( A )
h = a × sin( B )
c = ( a × sin( C ) ) ÷ sin( A)
c = ( b × sin( C ) ) ÷ sin( B)