Everything rests on one constant: 1 US gallon = 128 fl oz. Your tank holds tank_gal × 128 fl oz total; the concentrate occupies part of that, and water fills the rest.

tank_oz   = tank_gal × 128
oz/gal    concentrate_oz = rate × tank_gal
%         effective oz/gal = % × 1.28      (128 / 100)
          concentrate_oz   = (% × 1.28) × tank_gal
1:X       headline (trade) = 128 / X  oz/gal
          concentrate_oz   = (128 / X) × tank_gal
          exact footnote   = tank_oz / (X + 1)
water_oz  = tank_oz − concentrate_oz      (never above tank_oz)
spoons    1 fl oz = 2 tbsp = 6 tsp

The 1:X choice, shown both ways. The trade reads 1:32 as 128 / 32 = 4 oz/gal. The literal concentrate-to-total reading is 128 / 33 ≈ 3.88 — about 3 % stricter. We headline the trade number techs expect and footnote the exact value, rather than silently picking one.

Measurable spoons. Small amounts step down automatically: fl oz at 1 oz or more, tablespoons from 0.5–1 oz, teaspoons below that. In metric the concentrate shows mL. Water never rounds up past your tank.

Quick check (matches common labels): 1:32 → 4 oz/gal, 2 oz/gal → 1:64, 2 % → 2.56 oz/gal. A 4-gallon backpack at 1.5 oz/gal needs 6.0 fl oz of concentrate and 506 fl oz of water.

Sources: pesticidestewardship.org and onlinepestcontrolcourses.com (the 128 fl oz/gal basis and ×1.28 factor); AgentCalc (concentrate-plus-water output); TheYieldGrid (oz/gal + fl oz→tbsp→tsp stepping, usable-capacity guidance).