EOQCalculator.com
Wilson EOQ, with the math
The sawtooth inventory cycle (Q drops to 0, jumps to Q, repeats)
ROPcycle 1cycle 3cycle 5Q*
EOQ Calculator

The Wilson Q*, with the cost curve it sits on.

Enter annual demand, order cost, unit cost, and carrying-cost percent. You get Q*, the annotated U-curve, and the sensitivity strip that lets you defend the answer to a CFO.

Inputs
H = i × C$10 / unit / year
Cycle time T*13.7 days
Orders / year26.6
Optimal Q*
452
units per order
Annual holding
$2,258
Annual ordering
$2,258
Annual total (excl. purchase)
$4,517
Annotated cost curve
Holding (Q/2)HOrdering (D/Q)STotal
Q* = 452Total cost minimised at Q*, where holding and ordering curves cross.$/yrOrder quantity Q
Sensitivity (Q* at i +/- 3 pp)
i = 22%
481
i = 25%
452
i = 28%
427
The cost curve is flat near Q*: a 3-point i shift moves Q* on the order of 6 to 7 percent.
Direct answer

The EOQ calculator returns Q* = sqrt(2DS/H), the order size that minimises the sum of annual holding and ordering costs under constant demand D, fixed order cost S, and unit holding cost H = i*C. The cost curve is flat near Q*: a three-point swing in carrying-cost percent moves Q* by roughly six to seven percent[1].

What this site does that the others don’t.

Most EOQ calculators on the web return a number. We return the number, the curve it sits on, the sensitivity strip that tells you whether the number survives a 3-point carrying-cost shift, and the textbook derivation with sources you can footnote in a board pack. The math traces to Harris (1913)[2] and Wilson (1934)[3], with the German parallel derivation by Andler (1929)[4].

optimal order quantity
Q* = sqrt( 2 * D * S / H ) where H = i * C
Wilson EOQ in compact form.

Five linked calculators.

Read the derivation.

The Wilson formula has five derivation steps. We’ve laid them out as a linear spine so you can read forward, screenshot whichever step a CFO challenges, and cite the page.

  1. 1. Total cost function TC(Q) = (D/Q)S + (Q/2)H
  2. 2. First derivative dTC/dQ = -DS/Q^2 + H/2
  3. 3. Solve for Q* = sqrt(2DS/H)
  4. 4. Second derivative > 0 (confirm minimum)
  5. 5. Extend to price-break schedules

When EOQ is the wrong tool.

EOQ assumes constant demand, instantaneous resupply, no quantity discounts, and unlimited shelf life. Where those break: fashion apparel with markdown risk, perishables with shelf-life caps, short-lifecycle electronics with obsolescence loaders, MRO spares with intermittent demand. Those are the scenarios we model on dedicated pages so you can see where the model bends and what to use instead.