ALGEBRA & PERCENT percent change = (new − old) / old × 100 x = (c − b) / a from ax + b = c

GEOMETRY circle: C = πd = 2πr A = πr² cylinder volume = πr²h right triangle: a² + b² = c² sin = opp/hyp cos = adj/hyp tan = opp/adj sine bar: h = L sin θ

CONVERSIONS 1 in = 25.4 mm exactly 1 in = 25 400 µm 1 µin = 0.0254 µm 1 mm = 0.03937 in 1 ft = 12 in °F = 1.8°C + 32 °C = (°F − 32) / 1.8

STATISTICS x = Σx / n R = xmax − xmin s² = Σ(x − x)² / (n − 1) s = √s² z = (x − μ) / σ empirical: ±1s ≈ 68% ±2s ≈ 95% ±3s ≈ 99.7%

CAPABILITY & 10:1 Cp = (USL − LSL) / 6σ Cpk = min((USL − x)/3σ, (x − LSL)/3σ) gage resolution ≲ tolerance span / 10 cal standard ≲ gage resolution / 10

GD&T Bonus @ MMC = |actual size − MMC size| Allowed position = FCF tolerance + bonus (+ datum shift if a datum is also MMC) Position Ø error = 2 × √(Δx² + Δy²) Axis 0.003 off in X and 0.004 off in Y → radial 0.005, diameter error 0.010

METROLOGY RULES 10:1 — inspection discrimination ≈ 1/10 of the tolerance calibration standard ≈ 1/10 of the inspection equipment Reference temperature 20 °C / 68 °F Steel expansion ≈ 6.5 µin/in/°F (11.7 µm/m/°C) GR&R guideline: <10% good · 10–30% maybe · >30% not acceptable 0.0001 in ≈ 2.54 µm