Volatility Calculator
Turn a series of prices or returns into a standard deviation, annualised over the periods per year you choose.
Historical volatility is the sample standard deviation of returns over a stretch of data that has already happened. This volatility calculator produces that figure from a series you type in yourself — either a column of closing prices, which it converts into periodic returns first, or a column of returns you already have — and reports it twice: on the scale of the periods you supplied, and as an annualised volatility.
Formula: annualised volatility = standard deviation of periodic returns x sqrt(periods per year)
Your figures
Prices are converted into periodic returns first. Returns are used as they are.
Only used when the series holds prices. Log returns add across time; simple returns are what a statement shows.
The scale the annualised figure is quoted on: 252 for trading days, 52 for weeks, 12 for months.
Only used when the frequency is set to Custom.
Results
Annualised volatility
18.86%
from 5 periodic returns at 252 periods a year
- Volatility per periodThe sample standard deviation of the returns themselves, before any annualisation.
- 1.1881%
- Periods in a yearAnnualising multiplies the periodic figure by the square root of this.
- 252
- Mean return per periodThe centre the deviations are measured from. Volatility is unchanged by moving it.
- +0.4221%
- Highest return in the series
- +1.5015%
- Lowest return in the series
- -0.8929%
- Returns measured6 prices give 5 returns — one fewer, because the first price has nothing before it.
- 5
- Return definition usedEach return is the price ratio less one.
- Simple
What this means
The 5 periodic returns have a sample standard deviation of 1.1881%, and multiplying that by the square root of 252 puts it on an annual scale at 18.86%. Volatility measures dispersion in both directions and nothing else: the +1.5015% best period and the -0.8929% worst one both push it up by however far they sit from the +0.4221% mean. Which way the series actually went is the mean's job to report, not this figure's.
- Standard deviations here use the sample denominator, n − 1, which is the convention performance statistics are quoted under. On a short record the difference is visible: over twelve returns the sample figure is around 4.5% larger than the population one.
- Scaling a volatility across time uses the square-root-of-time rule, which holds when returns are independent from one period to the next. Real series trend and mean-revert, so a market that grinds one way understates the figure and one that whips back and forth overstates it.
- Measured only on the values entered. Anything that happened between two entries is invisible to the calculation, so more frequent values give a more faithful figure.
- Simple and logarithmic returns give different standard deviations from the same prices. Whichever is chosen, comparing this figure with another one means checking that the other was measured the same way.
Annualised volatility: 18.86%
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Continue with these figures
About the Volatility calculation
The measure is deliberately blind to direction. A period finishing 4% above the average of the series contributes exactly as much as one finishing 4% below it, because both are squared before they are added. That symmetry is what makes volatility a description of dispersion rather than of performance, and it is also where most misreadings start: a series that only ever rose can carry a high volatility, and one that ground steadily downwards can carry a low one.
Annualising is a convention rather than a fact about the market. Multiplying the periodic figure by the square root of the periods in a year assumes each period's return is independent of the one before it, which real series only approximately are. The calculator applies the rule because it is the convention every quoted volatility follows, and shows the periodic figure beside it so the assumption stays visible rather than buried.
Volatility formula
from a price series, one return per consecutive pair:
simple r_i = (P_i ÷ P_i−1) − 1
log r_i = ln(P_i ÷ P_i−1)
mean m = Σ r_i ÷ n
periodic σ = √( Σ (r_i − m)² ÷ (n − 1) )
annualised σ = periodic σ × √(periods per year)- P_i
- The i-th value in the series. n prices give n − 1 returns, because the first price has nothing before it to be compared against.
- m
- The arithmetic mean of the periodic returns — the centre each deviation is measured from. Moving it does not change the spread around it.
- n − 1
- The sample denominator. One degree of freedom is spent estimating m from the same returns the deviations are taken from.
- periods per year
- How often the series is sampled: 252 trading days, 365 calendar days, 52 weeks, 12 months, or a figure you enter under Custom.
Squaring each deviation before averaging is what makes the measure symmetric, and it is also what lets large deviations dominate: a period twice as far from the mean contributes four times as much. Taking the square root at the end undoes the units, so the answer comes back in percentage points and can be read directly against the returns that produced it.
The denominator is n − 1 rather than n because the mean subtracted inside the sum was itself estimated from those same returns. Dividing by n would understate the spread systematically. On a long record the choice is invisible; across twelve monthly returns the sample figure is around 4.5% larger than the population one, which is enough to move a Sharpe ratio in its first decimal place.
The annualisation multiplies by the square root of the periods in a year rather than by the periods themselves because variance, not standard deviation, is what adds across independent periods. Two independent days each carrying variance v give 2v between them, so the standard deviation of the pair is √2 times one day's rather than twice it. A daily figure of 1.19% therefore annualises to about 18.9% and not to 300%.
Simple and logarithmic returns give different answers from the same prices, and the gap widens with the size of the moves: ln(1.30) is 0.262, not 0.30. Log returns add across time, which is what makes the square-root scaling internally consistent and why option models are built on them, while simple returns are what a statement shows and what adds across positions. Neither is wrong, but comparing two volatilities means checking that both were built the same way.
Volatility: a worked example
Six daily closes — 100.00, 100.80, 99.90, 101.40, 100.60, 102.10 — read as simple returns and annualised over 252 trading days.
- Five periodic returns+0.8000%, −0.8929%, +1.5015%, −0.7890%, +1.4911%
- Mean return per period2.1107 ÷ 5 = +0.4221%
- Sum of squared deviations5.6463
- Sample variance5.6463 ÷ (5 − 1) = 1.4116
- Volatility per period√1.4116 = 1.1881%
- Annualised volatility1.1881% × √252 = 18.86%
1.1881% a day, or 18.86% a year. The series finished higher than it started, and that has no bearing at all on the figure: the two down days and the three up days each push it up by however far they sit from the +0.4221% mean. Six prices is also far too short a record for the estimate to be stable — it is shown here because the arithmetic can be followed by hand.
How to use the Volatility calculator
- Say what the series holds. Prices or equity values are converted into periodic returns first; periodic returns in percent are used exactly as entered.
- Enter the values oldest first, one per row. Blank rows are ignored, so a row added and not yet filled in will not blank the result.
- Choose a return definition if you entered prices. It is ignored when the series already holds returns, and the result panel states which one was used.
- Set the periods in a year to match how the series is actually sampled — 252 for daily bars, 52 for weekly, 12 for monthly, or your own number under Custom.
- Read the volatility per period alongside the annualised figure. The first is what the series shows; the second is the first scaled by an assumption about independence.
- Check the highest and lowest return rows. On a short series a single extreme period is often most of the volatility, and those two rows are where it shows up.
Limitations of the Volatility calculator
Every calculation makes assumptions. These are the ones that matter here.
- A standard deviation built from twenty or thirty observations carries a wide confidence interval. Two adjacent windows of the same series routinely differ by a third, and neither of them is the true figure.
- Annualising assumes returns are independent from one period to the next. A market that trends persistently is less volatile annually than the rule implies, and one that whips back and forth is more.
- Only the values entered are measured. An intraday spike or a gap that reversed between two rows is invisible, so monthly data reports a smaller figure than daily data over the same record.
- The measure is symmetric and cannot separate upside dispersion from downside. Downside deviation, which the Sortino ratio calculator uses, is the statistic that makes that distinction.
- This is historical volatility — a description of a finished sample. It is not implied volatility, which is what the options market is charging for movement that has not happened yet, and the two frequently disagree.
- Simple and logarithmic returns produce different standard deviations from identical prices, so a figure from here is only comparable with another one built on the same definition.
Frequently asked questions about Volatility
Why is the annualised figure so much larger than the daily one?
Because it is multiplied by the square root of 252, which is about 15.87. A 1.19% daily standard deviation becomes roughly 18.9% annualised. The multiplier is the square root of the period count rather than the period count itself, because variance is the quantity that adds across independent periods.
Should I enter simple or logarithmic returns?
Both are offered because practitioners genuinely disagree. Log returns add across time, which makes the square-root-of-time annualisation internally consistent, and they are what the lognormal model beneath option pricing assumes. Simple returns are what a brokerage statement shows and what adds across positions in a portfolio. On calm daily data the two differ in the third decimal; on a series containing a 30% day they visibly do not.
How many observations does a historical volatility calculator need?
More than most people have to hand. The standard error of a standard deviation falls with the square root of the sample size, so going from 20 observations to 80 roughly halves it. Under about thirty observations the figure should be read as an indication rather than a measurement, and it will move noticeably each time a row is added.
Why does volatility not tell me whether the series went up or down?
Because every deviation is squared before it is summed, which destroys the sign. Direction is the job of the mean return per period, reported as its own row. A series can rise 40% and show a high volatility, or fall 40% and show a low one, and neither case is a fault in the calculation.
Is this a realised volatility calculator or an implied volatility one?
It is a realised volatility calculator: the figure is computed backwards from prices that have already printed. Implied volatility is solved forwards out of an option's traded price and represents what the market is charging for movement between now and expiry. The implied volatility calculator handles that direction, and a persistent gap between the two is a normal feature of option markets rather than an error.
What should I enter for periods in a year on an unusual schedule?
Whatever the series actually is. If a strategy trades twice a week, 104 is the honest figure; if a fund reports over 200 dealing days, enter 200 under Custom. The number only has to describe how many of your periods fit into a year, and nothing on the page assumes 252 unless it is selected.
Last reviewed . See our methodology and editorial policy.
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