Calculations

How to Calculate Spring Rate, Coil Feed Yield, and Stamping Throughput

Work the five formulas that govern precision spring and stamping engineering, from k = Gd^4/(8D^3 Na) to rolled throughput yield, with real units and worked examples.

Five calculations carry most of the engineering load in precision spring and stamping work: spring rate, coil feed yield, press throughput, progressive die scrap rate, and dimensional yield. Each one takes inputs you already have, wire certs, strip dimensions, press counters, and SPC data, and turns them into numbers you can defend in a design review or a contract review. This guide works each formula with real units and a worked example, and flags where the input data should come from. If you want to skip the arithmetic, the Coil Feed Yield, Spring Rate Variation, and Dimensional Yield calculators run the same math with your inputs.

Compression spring rate follows k = G d^4 / (8 D^3 Na), where G is shear modulus, d is wire diameter, D is mean coil diameter, and Na is active coils. Take music wire with G = 11.5 x 10^6 psi, d = 0.032 in, D = 0.250 in, Na = 8. The numerator is 11.5 x 10^6 x 1.049 x 10^-6 = 12.06. The denominator is 8 x 0.01563 x 8 = 1.0. Rate is 12.1 lbf/in, or 2.11 N/mm. Pull G from the material spec, not from memory: 11.85 x 10^6 psi for chrome silicon, about 10.0 x 10^6 psi for 302 stainless.

The d^4 term dominates tolerance behavior. A 1 percent shift in wire diameter moves rate 4 percent, while a 1 percent shift in mean coil diameter moves it 3 percent the other way. Standard wire tolerance of plus or minus 0.0003 in on 0.032 in wire is 0.94 percent, worth 3.8 percent of rate by itself. Add coil diameter scatter and active coil count variation and a commercial spring lands near plus or minus 10 percent on rate, while precision grades hold 5 percent. The Spring Rate Variation calculator sums these contributions so you can see which input to tighten before you argue with the wire mill.

Strip utilization is part material over consumed material: yield = blank area / (progression pitch x strip width). A connector blank of 380 mm^2 running at 26.5 mm pitch in 40 mm wide strip consumes 1,060 mm^2 per hit, so utilization is 380 / 1,060 = 35.8 percent. Then subtract coil end losses: 1.5 m of threading scrap plus an unusable tail on every 500 m coil trims another 0.5 to 1 percent. The Coil Feed Yield calculator converts this straight to buy weight: at 7.85 g/cm^3 and 0.3 mm thickness, that strip consumes 2.50 g per hit to make a 0.89 g part.

Press throughput starts at gross strokes: parts per hour = SPM x 60 x parts out per stroke. A press running 120 SPM with a single out die makes 7,200 gross parts per hour. Net output multiplies by uptime and quality: 7,200 x 0.80 uptime x 0.985 first pass = 5,674 good parts per hour. Pull SPM from the press counter, not the nameplate, because dies rarely run at rated speed. A two out die at 90 SPM beats a one out die at 150 SPM, 10,800 versus 9,000 gross per hour. The Stamping Press Throughput calculator handles multi out tooling and shift patterns.

Progressive die scrap has two parts. Engineered scrap is the skeleton, fixed by strip layout: at 35.8 percent utilization, 64.2 percent of every coil is skeleton by design. Process fallout is the variable piece: misfeeds, slug pulls, and burr rejects, typically 0.3 to 2 percent of gross strokes. Compute fallout as rejected hits divided by gross hits over a defined run, for example 4,100 rejects in 500,000 strokes = 0.82 percent. The Progressive Die Scrap calculator keeps the two streams separate, which matters because skeleton is a strip layout problem while fallout is a die maintenance and feed problem.

Dimensional yield comes from process capability. Cpk = min(USL - mean, mean - LSL) / 3 sigma. For a free length of 20.0 mm with a plus or minus 0.4 mm tolerance, a run centered at 20.05 mm with sigma = 0.11 mm gives (20.40 - 20.05) / (3 x 0.11) = 1.06. That predicts roughly 750 ppm out the top side, a 99.92 percent yield. Sigma must come from at least 30 consecutive parts measured on a calibrated gauge, not from a capability study run two years ago. The Dimensional Yield calculator translates Cpk into expected ppm and yield directly.

Finally, chain the yields. Rolled throughput yield multiplies first pass yield at every operation: 99.2 percent stamping x 99.0 percent heat treat x 98.5 percent plating x 99.8 percent final inspection = 96.5 percent. That means starting 1,036 pieces to ship 1,000, and the coil buy calculation should use the started quantity, not the order quantity. Batch operations add their own math: the Heat Treat Load calculator sizes furnace loads against fixture capacity, and an unbalanced load shows up later as yield loss at temper. Run these five calculations before quoting, then rerun them from actual data after the first production lot.

Published 2026-07-02.