What this calculator does
Everyone has a drawer of orphan socks. This calculator turns that feeling into a simple, transparent model so you can see roughly what a habit of losing socks costs. You enter how many loads you wash, how many socks are in a load, and your own guess of the chance that any single sock goes missing in one wash and dry cycle. It returns the expected number of socks lost per year, what that costs to replace, and how likely a given sock is to survive a year.
This is an estimate for fun, not a measurement. There is no reliable universal loss rate to plug in. The default of 0.5% per sock per wash is an illustrative assumption. Set it to whatever matches your household, for example by counting how many orphan socks you accumulate in a year.
The model
- Washes per year = loads per week × 52.
- Sock washes per year = washes per year × socks per load.
- Expected socks lost per year = sock washes per year × loss chance per wash. Losses are treated as independent events, so this is an expected value, not a guarantee.
- Pairs’ worth lost = socks lost / 2. Replacement cost = pairs’ worth × price per pair.
- Survival chance = (1 − loss chance)washes per year, the probability that one particular sock avoids being lost in every wash of the year.
Worked example
Using the defaults: 4 loads a week gives 4 × 52 = 208 loads a year. With 12 socks per load that is 208 × 12 = 2,496 sock washes. At a 0.5% chance per wash, the expected loss is 2,496 × 0.005 = 12.48 socks a year, or 6.24 pairs’ worth.
At $4 per pair the replacement cost is 6.24 × $4 = $24.96 a year. The chance a given sock survives all 208 washes is 0.995208 ≈ 35.3%, which shows how a small per-wash risk compounds. Over 10 years the model expects 124.8 socks lost and about $249.60 in replacements.
Reading the result, and limits of the model
- Lost socks and orphans are different. A lost sock leaves its mate without a partner. The pairs’ worth figure prices replacement as if every lost sock costs half a pair, which slightly overstates cost if you can re-pair leftovers.
- Socks are not equal. Small, light socks may be more likely to hide in a duvet cover or dryer seal. The model uses one average chance for all.
- Loss is not really independent. Some households lose socks in bursts, for example when travelling. Treat the result as a typical-year average.
- Cost is only the replacement price. It ignores the time spent searching or matching socks.
If the number surprises you, try a lower loss chance or wash socks in a mesh bag and see how the estimate changes. It is a way to reason about the problem, not evidence of what actually happens in your machine.