The per-side formula
For a 100 kg target on a 20 kg bar, subtract the bar to leave 80 kg, then divide by two: 40 kg per side. With standard plates that can be two 20 kg plates on each side.
Worked examples
- 105 kg on a 20 kg bar: 42.5 kg per side = 20 + 20 + 2.5.
- 140 kg on a 20 kg bar: 60 kg per side = 20 + 20 + 20.
- 225 lb on a 45 lb bar: 90 lb per side = 45 + 45.
- 315 lb on a 45 lb bar: 135 lb per side = 45 + 45 + 45.
Why some target loads are impossible
The smallest matching plate pair controls the total increment. If the lightest available plate is 1.25 kg, adding one to each side changes the total by 2.5 kg. A number between valid increments cannot be loaded symmetrically with that profile.
Competition and gym inventories differ. A calculator must know the unit, bar weight and available plate sizes before it can give an exact stack. It should never silently substitute a close load and label it exact.
Load largest plates first
After calculating the per-side target, use the largest plate that fits, subtract it and continue. This produces a compact stack and is the method Plate Stack uses with exact quarter-unit arithmetic rather than floating-point approximations.