Calculations

How to Calculate Feeder Rate, Dosing Accuracy, and Loss-in-Weight Metrics

A step-by-step walkthrough of the core weighing and dosing formulas, from gravimetric feed rate to dosing accuracy and hopper refill timing, with worked numbers.

Start with the base gravimetric feed rate. A loss-in-weight (LIW) feeder derives rate from the rate of change of hopper weight: Rate = (W1 minus W2) / (t2 minus t1). If the hopper reads 42.500 kg at t1 and 42.083 kg 5 seconds later, mass loss is 0.417 kg over 5 s, so 0.0834 kg/s, or 300.2 kg/h. Controllers sample this on a 20 to 100 ms loop and filter noise before comparing to setpoint. Use the Feeder Rate calculator to convert between kg/h, lb/h, and g/min, since recipe setpoints and PLC scaling rarely share units.

Dosing accuracy is a percentage error, not a raw weight. Error % = (actual minus target) / target times 100. A target dose of 25.00 kg that lands at 25.18 kg is +0.72%. For a batch you care about both mean bias and scatter: compute the standard deviation of, say, 30 consecutive doses, then the coefficient of variation, CV = (sigma / mean) times 100. A CV of 0.5% on a 25 kg dose means sigma is 0.125 kg. The Dosing Accuracy calculator returns bias, sigma, and CV together so you separate a calibration offset from genuine feeder instability.

Hopper refill interval tells you how long a filled hopper feeds before it hits the low-level trip. Interval = usable mass / feed rate. Usable mass = fill capacity minus refill-trigger level. A 120 kg hopper refilling at 30 kg (25% low trip) has 90 kg usable; at 300 kg/h that is 0.30 h, or 18 minutes between refills. Refills interrupt gravimetric control and force the feeder into volumetric mode for 10 to 40 seconds, so this interval sets your control-loss duty cycle. The Hopper Refill Interval calculator flags feeders that refill more than 3 to 4 times per hour.

During refill, the feeder cannot weigh, so it runs volumetric: it holds the last known screw speed to maintain approximate rate. The gravimetric-vs-volumetric delta quantifies the drift. Delta % = (volumetric rate minus gravimetric rate) / gravimetric rate times 100. If bulk density rose 3% since the last weigh, a volumetric hold over-delivers by roughly 3%. Over a 25-second refill inside an 18-minute cycle, that error is diluted to about 0.07% of the batch. The Gravimetric Vs Volumetric Delta calculator lets you test whether refill frequency plus density swing pushes you past tolerance.

LIW calibration ties screw speed to mass flow. You run the feeder at fixed RPM, capture mass loss over a timed window, and compute the feed factor: k = mass delivered / (RPM times minutes), in kg per revolution. If 12.0 kg falls over 4.0 minutes at 150 RPM, k = 12.0 / 600 = 0.0200 kg/rev. The controller inverts this to set RPM for any target rate: RPM = target rate / k. Rebuild the curve at 3 to 5 points because k drops at low speed from bearing drag. The Loss-In-Weight Calibration calculator fits the curve and reports linearity.

Batch tolerance defines the pass/fail window around a setpoint. Window = target times (1 plus or minus tolerance). A 500 kg batch at plus or minus 1.5% passes between 492.5 and 507.5 kg. For a multi-ingredient recipe, tolerances stack: if you dose eight ingredients each held to plus or minus 0.5%, the batch total variance is the root-sum-square, roughly 0.5% times the square root of 8, about 1.4%, not 4%. The Batch Tolerance Window calculator computes both the per-ingredient window and the combined RSS band so you do not over-tighten single feeders.

Microingredients need their own math because dose mass is tiny relative to feeder capacity. A 0.05% inclusion in a 1,000 kg batch is 0.500 kg. If your feeder resolution is plus or minus 20 g, that is a 4% relative error on the dose, far past a 1% target. Minimum reliable dose = resolution / target error. To hit 1% on a 0.500 kg dose you need resolution near 5 g, which points to a small twin-screw micro-feeder. The Microingredient Usage calculator sizes the feeder against required accuracy and flags doses too small for the loadcell.

Feeder utilization closes the loop between rate and schedule. Utilization % = actual running time / available time times 100. A feeder running 6.2 h of a 8 h shift is at 77.5%. Combine that with average delivered rate to get shift throughput: 300 kg/h times 6.2 h = 1,860 kg. Downtime buckets, refill dwell, changeover cleanout, and starvation from upstream, each subtract measurable minutes. The Feeder Utilization calculator splits available time into running, refill, and idle so you can see whether a rate shortfall is a speed problem or a scheduling problem.

Published 2026-07-01.