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 & Major Run
Calculate Minor Run
Minor Run = Major Run × ( tan(Major Pitch Angle) ÷ tan(Minor Pitch Angle))
Minor Run = Major Run × ( Major Pitch ÷ Minor Pitch)
Known Variables: Major Pitch Angle & Minor Pitch Angle & Minor Run
Calculate Major Run
Major Run = Minor Run × ( tan(Minor Pitch Angle) ÷ tan(Major Pitch Angle))
Major Run = Minor Run × ( Minor Pitch ÷ Major Pitch)
Known Variables: Major Pitch Angle & Minor Pitch Angle & Span
Calculate Major & Minor Runs
Major Run = ((Span × sin(Minor Pitch Angle)) ÷ sin (180 - Major Pitch Angle - Minor Pitch Angle)) × cos( Major Pitch Angle )
Minor Run = ((Span * sin(Major Pitch Angle)) ÷ sin (180 - Major Pitch Angle - Minor Pitch Angle)) × cos( Minor Pitch Angle )
Known Variables: Major Pitch Angle & Minor Pitch Angle & Span
Calculate Major & Minor Rise
Major Rise = ((Span × sin(Minor Pitch Angle)) ÷ sin (180 - Major Pitch Angle - Minor Pitch Angle)) × sin( Major Pitch Angle )
Known Variables: Major Pitch Angle & Minor Pitch Angle & Span
Calculate Major & Minor Rafter Lengths
Major Rafter = (Span × sin(Minor Pitch Angle)) ÷ sin (180 - Major Pitch Angle - Minor Pitch Angle)
Minor Rafter = (Span * sin(Major Pitch Angle)) ÷ sin (180 - Major Pitch Angle - Minor Pitch Angle)
Known Variables: Major Pitch Angle & Major Run & Span
Calculate Minor Pitch & Minor Run
Minor Pitch Angle = arctan((Major Run × sin(Major Pitch Angle)) ÷ (Span - Major Run ))
Minor Run = ((Span * sin(Major Pitch Angle)) ÷ sin (180 - Major Pitch Angle - Minor Pitch Angle)) × cos( Minor Pitch Angle )
Known Variables: Minor Pitch Angle & Minor Run & Span
Calculate Major Pitch & Major Run
Major Pitch Angle = arctan((Minor Run × sin(Minor Pitch Angle)) ÷ (Span - Minor Run ))
Major Run = ((Span × sin(Minor Pitch Angle)) ÷ sin (180 - Major Pitch Angle - Minor Pitch Angle)) × cos( Major 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)