Sharpe Ratio Calculator

Sharpe ratio = (return − risk-free rate) ÷ standard deviation of returns. Enter annual figures, or paste a series of returns to get the annualised Sharpe ratio, the Sortino ratio, maximum drawdown and an equity curve.

What do you have?

A series of returns Annual return and volatility

Sharpe ratio (annualised)–

Sortino ratio (annualised)–

Maximum drawdown–

Inputs Example values The numbers below are made up. Replace them with your own. Use a dot for decimals.

Returns per period (%)One per line, or separated by commas or spaces. 2.5 means +2.5%, -1.2 means −1.2%. Oldest first.

Return periodSets periods per year for annualising Daily (252/yr) Weekly (52/yr) Monthly (12/yr) Quarterly (4/yr) Annual (1/yr)

Risk-free rate (% per year)Converted to a per-period rate

Sortino target (MAR)Returns below it count as downside Risk-free rate 0%

Reset to example Clear

Returns counted (n)

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Mean return per period

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Risk-free rate per period

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Mean excess return per period

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Standard deviation per period (sample, n − 1)

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Sharpe ratio per period

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Sharpe ratio, annualised

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Downside deviation per period

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Sortino ratio (per period / annualised)

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Maximum drawdown

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Total compounded return

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Compound annual growth rate

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Everything runs in your browser. Nothing is saved or sent.

How to use the Sharpe ratio calculator

1. Pick a mode. If you already know the annual return and annual volatility (for example from a fund factsheet), choose “Annual return and volatility”. If you have a list of returns from a broker statement, a backtest or a trading performance report, choose “A series of returns”.
2. Paste returns as percentages, oldest first. Each value is the return of one period: 1.8 for +1.8%, -0.6 for −0.6%. A % sign after a number is fine.
3. Choose the period that matches the data. The calculator uses it to convert the risk-free rate and to annualise: 252 trading days, 52 weeks, 12 months, 4 quarters or 1 year.
4. Enter the annual risk-free rate, such as a Treasury bill yield in the same currency and over the same dates. Use 0 if you only want return per unit of volatility.
5. Read the results. The annualised Sharpe ratio is the headline. The Sortino ratio, maximum drawdown and the equity curve show what the Sharpe ratio leaves out.

Sharpe ratio formula

William F. Sharpe introduced the measure in 1966 as the “reward-to-variability ratio”. In his 1994 article “The Sharpe Ratio” (The Journal of Portfolio Management, Fall 1994) he defines the historic (ex post) version as the average differential return divided by the standard deviation of that differential return, and gives the spreadsheet form AVERAGE(C1:C60)/STDEV(C1:C60) for 60 differential returns in column C. This calculator follows that definition with the risk-free rate as the benchmark.

Why √k. If each period’s excess return is independent with the same mean and standard deviation, the mean over k periods is k × d̄ and the standard deviation is √k × s, so the ratio grows by k ÷ √k = √k. Sharpe’s article sets out the relation between one-period and multi-period ratios for serially uncorrelated returns and recommends measuring over fairly short periods, such as months, then annualising for comparison. He also notes that compounding and serial correlation make the real relationship more complicated.

Sortino target. The Sortino ratio needs a minimum acceptable return (MAR). CFA Institute’s article on the ratio lists an absolute return, an index return, the risk-free rate or zero as choices. This calculator defaults to the per-period risk-free rate, so the Sharpe and Sortino numerators match, and offers 0% as the alternative. With the 0% target the numerator is the plain mean return, not the excess return.

Worked examples

The return series below is fictional and only shows the arithmetic. Each example can be reproduced in the calculator.

1. Annual figures (Sharpe’s own stock-market illustration)

Sharpe’s 1994 article uses a 6% annual excess return and a 15% annual standard deviation, which gives an annual Sharpe ratio of 0.40. In quick mode, a 10% return, a 4% risk-free rate and 15% volatility reproduce it: (10 − 4) ÷ 15 = 0.40. That is the calculator’s quick-mode example.

2. Twelve monthly returns (the series-mode example)

Returns: 2.1, −1.4, 3.0, 0.8, −2.6, −1.9, 4.2, −0.7, 1.1, −3.1, 2.4, 1.6 (% per month), risk-free rate 4% per year, target = risk-free rate.

3. Sortino ratio check against a published example

Rollinger and Hoffman’s paper “Sortino: A ‘Sharper’ Ratio” (Red Rock Capital, hosted by CME Group) works through eight annual returns of 17, 15, 23, −5, 12, 9, 13 and −4% with a 0% target. The mean is 10%. Only −5% and −4% fall below the target, so downside deviation = √((0.05² + 0.04²) ÷ 8) ≈ 2.264% and Sortino ≈ 10 ÷ 2.264 = 4.417. Paste the same eight numbers, choose “Annual” and the 0% target, and the calculator returns 4.417. The Sharpe ratio of the same series with a 0% risk-free rate is about 1.02, because the large gains raise the standard deviation.

4. Edge cases the calculator handles

• Zero volatility (every return the same, or 0% volatility in quick mode): the standard deviation is 0, so the Sharpe ratio is not defined. The calculator says so instead of showing “infinity”.
• One return: a sample standard deviation needs at least two values, so only the mean, drawdown and total return are shown.
• No downside: if no return is below the Sortino target, downside deviation is 0 and the Sortino ratio is not defined. The calculator says that no period fell below the target.
• Losses of 100% or more in one period are rejected, because the equity curve would reach zero or go below it.

How to read the result

The Sharpe ratio is excess return per unit of total volatility. A positive value means the returns beat the risk-free rate on average; a negative value means they did not. A higher value means more excess return for each unit of volatility taken.

This page does not label results as good or bad. Thresholds that circulate online, such as “above 1 is good” or “above 3 is excellent”, are rules of thumb: the calculator pages reviewed for this tool give different bands, and one of them calls the cut-offs “of uncertain origin”. A Sharpe ratio means most when it is compared with another one measured over the same dates, with the same return period and the same risk-free rate.

• It is an estimate. Andrew Lo’s “The Statistics of Sharpe Ratios” (Financial Analysts Journal, 2002) shows that a Sharpe ratio from a sample has a standard error, and that serial correlation can overstate an annualised figure, by as much as 65 percent for one hedge fund in his study. A short series can produce a high ratio by chance.
• It treats gains and losses alike. Big up months raise the standard deviation as much as big down months. The Sortino ratio only penalises returns below the target.
• It ignores order. Mean and standard deviation do not change if the returns are shuffled, but the drawdown does. Read the maximum drawdown and the chart next to the ratio.
• Backtests flatter. A ratio from a backtest is only as good as the backtest: costs, slippage and the number of variants tried all matter.

Sharpe ratio vs Sortino ratio vs maximum drawdown

For the growth rate of a whole investment, use the CAGR calculator. For how risk per trade relates to the chance of a deep drawdown, see the risk of ruin calculator.

FAQ

How do you calculate the Sharpe ratio?

Subtract the risk-free rate from the return and divide by the standard deviation of returns: Sharpe ratio = (Rp − Rf) ÷ σ. Example: a 10% annual return, a 4% risk-free rate and 15% annual volatility give (10 − 4) ÷ 15 = 0.40. From a series of returns, take the average excess return per period, divide it by the sample standard deviation of the excess returns, then multiply by the square root of the number of periods per year to annualise.

What is a good Sharpe ratio?

There is no official threshold. Calculator sites often quote bands such as “above 1 is good”, but they rarely cite a source and the bands differ from site to site. The ratio is most useful for comparing strategies or funds measured over the same dates, with the same return frequency and the same risk-free rate. Andrew Lo (Financial Analysts Journal, 2002) showed that an estimated Sharpe ratio carries sampling error and that serial correlation can overstate an annualised figure, by as much as 65 percent for one hedge fund in his study.

How do you annualize a Sharpe ratio?

Multiply the per-period Sharpe ratio by the square root of the number of periods per year: √252 for daily returns (trading days), √52 for weekly, √12 for monthly and √4 for quarterly. The mean excess return grows with the number of periods and the standard deviation with its square root, if returns are independent from one period to the next. Lo (2002) warns that monthly Sharpe ratios cannot be annualised by multiplying by √12 except under very special circumstances, so treat the result as an approximation when returns are serially correlated.

What is the difference between the Sharpe ratio and the Sortino ratio?

The Sharpe ratio divides excess return by total volatility, so large gains count as risk too. The Sortino ratio divides the return above a target, the minimum acceptable return (MAR), by downside deviation, which only counts returns below that target. CFA Institute's article on the Sortino ratio gives the formula as (mean portfolio return − MAR) ÷ downside deviation. Downside deviation squares each shortfall below the target, averages over all periods (periods at or above the target count as zero) and takes the square root.

What risk-free rate should I use for the Sharpe ratio?

Use the yield on a short-term government bill in the same currency and over the same dates as the returns, for example the Treasury bill rates the U.S. Department of the Treasury publishes each business day for US dollar returns. Enter it as an annual rate. The calculator converts it to a per-period rate with (1 + annual rate)^(1 ÷ periods per year) − 1 and subtracts it from every return.

Can a Sharpe ratio be negative?

Yes. It is negative whenever the average return is below the risk-free rate. Negative values are hard to rank: with a negative numerator, a more volatile series gets a ratio closer to zero, so the less negative of two negative Sharpe ratios is not automatically the better result. Compare the excess returns and the volatility separately in that case.

Should you use sample or population standard deviation for the Sharpe ratio?

This calculator uses the sample standard deviation, which divides by n − 1, the same method as Excel's STDEV.S. Sharpe's 1994 article gives the spreadsheet example AVERAGE(C1:C60)/STDEV(C1:C60) and notes that either version can be used when every fund is measured over the same number of periods, because the ranking does not change. The two differ by a factor of √(n ÷ (n − 1)), about 4% for 12 returns and under 0.2% for 252.

Does the Sharpe ratio show drawdowns?

No. The Sharpe ratio uses only the average and the standard deviation, so the order of the returns does not matter: shuffle a series and the Sharpe ratio stays the same while the maximum drawdown can change a lot. That is why this calculator also shows the maximum drawdown, the largest fall from a peak in the compounded equity curve.

Related tools and templates

• CAGR calculator
  Compound annual growth rate between two values.
• ROI calculator
  Return on investment, total and annualised.
• Risk of ruin calculator
  How risk per trade affects the chance of a deep drawdown.
• Trading performance report template
  Collect periodic returns to paste into this calculator.
• Investment tracker template
  Track holdings and returns over time.

Sources

1. William F. Sharpe, “The Sharpe Ratio”, The Journal of Portfolio Management, Fall 1994 (author’s Stanford page). Definition, spreadsheet form, time dependence, 0.40 example.
2. Andrew W. Lo, “The Statistics of Sharpe Ratios”, Financial Analysts Journal 58(4), 2002 (CFA Institute). Sampling error and annualisation with serial correlation.
3. Deborah Kidd, CFA, “The Sortino Ratio: Is Downside Risk the Only Risk that Matters?”, CFA Institute, 2012. Sortino formula, MAR choices, downside deviation over all periods.
4. Thomas N. Rollinger and Scott T. Hoffman, “Sortino: A ‘Sharper’ Ratio”, Red Rock Capital (CME Group education library). Target downside deviation and the eight-year worked example.
5. Microsoft Support, STDEV.S function. “The standard deviation is calculated using the "n-1" method.”
6. U.S. Department of the Treasury, Daily Treasury Bill Rates. A source for a US dollar risk-free rate (no rate is pre-filled from it).

All sources retrieved 3 Nov 2026.

Educational tool only, not financial or investment advice. Results are arithmetic on the numbers you enter. Past returns and ratios computed from them do not predict future returns. All example returns and rates on this page are hypothetical except where a published source is named.