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5-inch or 6-inch? The roof area and pitch decide, not the price.
Gutters overflow because they were undersized, not because they were dirty. Sizing is drainage math: roof footprint times a pitch factor gives adjusted area, and that number maps to 5-inch or 6-inch K-style capacity. This calculator runs it, adjusts for heavy-rainfall regions, and counts the downspouts your run actually needs.
Homeowners getting gutter quotes use this to know whether they need 5-inch or 6-inch before the upsell conversation, and how many downspouts the run demands. The pitch factor is the part every free estimator skips — steep roofs need bigger gutters, full stop.
When adjusted drainage area exceeds ~5,500 sq ft (heavy-rain regions: ~4,400), on steep roofs (9/12+), or on long runs where one downspout can't keep up. A 6" K-style carries roughly 40% more water than a 5". The upgrade cost is small; the fascia-rot cost of overflow is not.
At least one per 30 feet of gutter run AND one per ~600 adjusted square feet — whichever demands more. A 120-ft run needs 4 by spacing alone. Long runs with too few downspouts are the classic overflow setup even with correctly sized gutters.