What your roof pitch actually costs you
Why pitch is measured in rise over run, not degrees
Roofers and building permits describe slope as a ratio, like 6/12, meaning the roof rises 6 inches for every 12 inches of horizontal run. Converting to the tilt angle solar tools use takes the arctangent of that ratio. A 6/12 pitch works out to about 26.6 degrees, a 4/12 pitch to about 18.4 degrees, and a 10/12 pitch to about 39.8 degrees. If changing the pitch itself during a reroof is on the table, the roof pitch change for solar cost estimator prices that option out directly.
Why most roofs need little or no adjustment
Production loss from a non-optimal tilt grows with the square of the miss, so it is gentle near the optimum and steep far from it. At this calculator's fit, a pitch 10 degrees from the optimal angle loses about 1.2% of annual output, 15 degrees about 2.6%, and 30 degrees about 10%. At latitude 40, a 6/12 roof loses about 0.6%, a 4/12 roof about 2.6%, and a 2/12 roof about 6.7%. Climate shifts the curve a little, since sunnier sites gain more from an optimal tilt than cloudier ones. The tilt angle optimizer shows your exact optimal angle and how far your pitch sits from it. NLR's PVWatts system design documentation explains how tilt enters the modeled output, so the curve above is the same one professional estimates use.
When adding panels beats correcting the angle
Tilt-up racking adds hardware, wind engineering, and roof penetrations, so the question is what it recovers. At latitude 40, a 2/12 roof loses about 6.7%, which tilting up to the optimum could recover as about 880 kWh a year on a 10 kW system, roughly $160 at 18.4 cents per kWh. A 4/12 roof loses only 2.6%, about 340 kWh or $63 a year. NLR's PVWatts calculator lets you check the gain at your own address by running your roof pitch and the optimal tilt side by side. For most residential roofs, adding one or two panels to offset a pitch-driven gap is cheaper than adjustable racking, unless the pitch is far off, and the usable roof area calculator confirms your roof has room for them.
Where azimuth fits into this picture
Roof pitch is only half the orientation story. A roof facing east or west loses about 16% at a typical 6/12 pitch from azimuth alone, far more than most pitch mismatches cost. The two effects interact too, since the loss from facing away from south grows with pitch, from about 7% on a 2/12 roof to 22% on a steep 12/12 roof facing east or west. The roof azimuth orientation calculator takes pitch into account, and the annual kWh output estimator shows full-year production once both are settled.