Barbell Plate Inventory Loader
Find the heaviest symmetric plate load that fits your inventory without exceeding an entered target.
YOUR CALCULATION
Result
—
Calculation steps
Work through one step at a time or reveal the complete calculation. The steps use your current inputs.
How to calculate
Use bounded integer optimization on one side, then mirror each selected plate pair.
Loaded mass=fixed mass+2×sum(one plate mass×selected pair count) ≤ entered target
Worked example
With a 20 kg fixed bar and one pair each of 20, 10 and 5 kg plates, the greatest load at or below 100 kg is 90 kg.
Assumptions and input details
All masses use one chosen unit with 0.25-unit increments. Inventory counts mean matching pairs, not individual plates. Fixed mass includes all collars. The result chooses equipment arithmetic only and does not recommend a load or assess lifting safety or equipment compatibility.
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Results use floating-point arithmetic and displayed rounding. Read the formula, assumptions and any stated data precision before interpreting the result.
Is my input uploaded?
The calculation runs in your browser. No account, file upload or external AI service is required. Inputs are not saved between page reloads.
Count ordered or unordered selections, with or without repetition. Read the exact integer result, compare all four cases and list examples for small problems.
Aggregate sets, repetitions and external-load volume by exercise label.
Convert mph, km/h, knots and meters or feet per second or minute.
Reserved advertising space.