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The expanded practical toolkit

Numbers, with
their limits showing.

Eight ways to test the arithmetic behind an idea. Every tool states what it models, what it leaves out and where a clean answer can become misleading.

The practical toolkit connects arithmetic inputs to a result while making uncertainty and risk explicit.

Test the inputs before trusting the output

Write down what each number measures: price per unit is not total position value, and a percentage is not a cash amount. Check whether a cost is already included in a price or must be entered separately. An unknown input is not automatically zero.

Save one baseline calculation, then change one uncertain assumption and compare the results. This reveals which input is doing the most work. Keep the assumptions with the answer: the calculator checks a simplified relationship, not whether a trade can be executed or what the largest possible loss will be.

Position size

How many whole units fit inside a planned risk budget? Use one currency consistently.

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Units = floor((equity × risk %) / (|entry − stop| + per-unit costs)). For shares or simple unit-based spot products. Not a forex-lot, futures-contract, options or margin calculator. A gap or slippage can exceed planned risk; notional exposure may exceed available capital.

Risk & reward

Compare a planned target with a planned stop, after estimated round-trip costs.

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Net reward = |target − entry| − costs. Planned risk = |entry − stop| + costs. Breakeven win rate = 1 / (1 + net reward / risk). Assumes fixed win/loss outcomes and identical costs; fills and outcomes will vary. A higher ratio is not proof of a better trade.

The climb back

A loss and an equal percentage gain do not cancel each other out.

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Required gain = drawdown / (100 − drawdown) × 100. This describes recovery to the original nominal balance, ignoring contributions, withdrawals, taxes and inflation. It is not a forecast.

Trade expectancy

Look past win rate. The size of wins and losses matters, too.

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Expectancy = win probability × average win − loss probability × average loss − average cost. Input gross wins/losses so costs are not double-counted. Historical estimates are uncertain, especially in small samples. A positive result is not a guarantee.

FX units & pip value

Convert a stop distance into base-currency units using an explicit quote-to-account conversion.

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Units = floor(budget / (stop pips × pip size × conversion + per-unit cost) / increment) × increment. Pip value = units × pip size × conversion. For linear FX exposure only, not options. For a USD account trading EUR/USD, conversion is 1; other quote currencies need a current independently verified rate. Excludes margin limits and changing conversion rates. Gaps and liquidation can exceed the estimate.

Portfolio shock scenario

Apply one simultaneous shock to three unleveraged holdings, with residual cash unchanged.

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P/L = sum(holding value × shock). Holdings must total no more than equity; the remainder is cash. This is a chosen scenario, not a probability estimate or value-at-risk model. No leverage, derivatives, FX conversion, fees, tax or rebalancing. It assumes all holdings can be valued at the scenario marks; a real exit may be worse.

Cost-aware break-even

Find the sale price needed to recover entry price and specified round-trip friction on a long position.

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Break-even sale = [entry × (1 + entry fee %) + fixed fees / units + friction per unit] / (1 − exit fee %). All monetary inputs use one currency. Enter spread/slippage only if not already embedded in your price assumptions; do not double-count. Excludes financing, tax, changing FX and minimum-fee rules. This is a simple long cash position, not an option or leveraged-contract model.

Win-rate uncertainty

A sample win rate looks precise. Its uncertainty often tells a more useful story.

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Approximate 95% Wilson score interval using z = 1.959964. Assumes independent Bernoulli trials with one stable win probability, no selection bias and a pre-specified strategy. Correlated trades, regime changes and strategy selection can invalidate that interpretation. The interval concerns win probability, not profit or future drawdown; payoff size and costs remain essential.

All calculations run in this browser. Nothing you enter is submitted. Default values are examples, not suggested allocations, leverage or risk limits. Use one currency consistently unless a conversion is explicitly requested.

METHODS & CONTEXT

NIST: confidence intervals for proportions ↗Investor.gov: how fees and expenses affect a portfolio ↗