Plate Math

Plate Math solves the everyday friction of loading a barbell: you have a target weight, you need to know which plates go on each side. The calculator handles both imperial and metric, accounts for the bar weight, and confirms the full loaded total. It also enforces sleeve capacity — if a combination is physically impossible to fit on the bar, it won’t suggest it.

The core of the calculator is a constrained variant of the coin-change problem: find the plate combination that hits a per-side target. The textbook greedy approach — always take the largest plate that fits — works for a complete plate set but breaks against a real gym inventory, where you might have four 45s and no 25s. The solver works from a configurable inventory of available plates per side rather than assuming infinite supply, and falls back to the closest achievable weight when an exact match isn’t possible, since “you can’t make exactly 137.5 here” is a more useful answer than no answer.

Three modes share that solver. The standard calculator returns the combination for a target weight; the interactive builder lets you add plates one at a time and watch the total accumulate; the percentage mode takes a one-rep max and generates loadouts from 100% down to 50%, mapping to how percentage-based strength programs are actually written. All three are a single component driven by a mode flag, so the solver and the visual barbell renderer — which draws the plate stack on each sleeve with per-side counts — stay shared rather than duplicated across three screens. Sleeve-capacity logic caps each side so the renderer never shows a physically impossible stack.