What this calculator answers
For a trade with a stop-loss and a take-profit, this calculator divides the possible reward by the possible risk. You enter the entry, the stop-loss and the take-profit. The page works out whether the trade is a long or a short from where the stop sits: below the entry is a long, above it is a short. It also shows the win rate at which the average trade would break even.
The formula
r = |E − S|, w = |T − E|, R = w / r, b = r / (r + w), a = r / E, c = w / E, X = n·r, Y = n·w
E is the entry price, S the stop-loss and T the take-profit. r is the risk per unit and w the reward per unit. R is the reward divided by the risk, and b is the break-even win rate. a and c are the risk and the reward as a share of the entry. n is the quantity, X the total risk and Y the total reward.
To see where b comes from, say a trade wins with probability p. The average result is zero when p × w equals (1 − p) × r, which gives p = r / (r + w).
A worked example
Take a long with an entry of $100.00, a stop-loss of $95.00 and a take-profit of $115.00. The risk per unit is $5.00 and the reward per unit is $15.00. The ratio is 1 : 3.00. The break-even win rate is 25%. The risk is 5% of the entry and the reward is 15%.
Now add a quantity of 50 units. The total risk is $250.00 and the total reward is $750.00. A short works the same way, with the stop-loss above the entry and the take-profit below it. These numbers show only the arithmetic. They are not a suggestion for any trade.
What the result does not include
The result leaves out fees, spreads and slippage, and it assumes the stop fills at your price. If the market gaps through the stop, the real loss can be larger than the one shown. The break-even win rate is the rate at which the average trade neither gains nor loses. It is not a forecast of how often you will win. The ratio also says nothing about how likely the target is to be reached before the stop.
Related
To turn a risk amount into a number of shares or units, use the position size calculator. To size a stake from your win rate and payoff, see the Kelly criterion calculator.
FAQ
What is a risk/reward ratio?
It compares the potential loss on one trade with its potential gain. This page shows it as 1 followed by the reward for each 1 of risk, so a risk of $5.00 against a reward of $15.00 reads 1 : 3.00.
What win rate do I need to break even?
It is the risk divided by the risk plus the reward. At 1 : 3.00 that is 25%, before fees and slippage. It is the rate at which the average trade gains and loses nothing, not a forecast of your results.
How does the calculator know whether the trade is a long or a short?
It reads the stop-loss. A stop below the entry is a long, and a stop above it is a short. The take-profit must then sit on the other side of the entry, and the page shows an error if it does not.
Does the ratio include fees and slippage?
No. Fees, spreads and slippage raise the real risk and lower the real reward, so the true ratio is somewhat worse than the one shown.