Expected Move Calculator

Work out the move an option's implied volatility prices in over a given number of days, with one and two standard deviation ranges.

Implied volatility is quoted as an annualised percentage, which is almost never the horizon anyone is actually trading, and an expected move calculator exists to close that gap. An option with three weeks left does not carry a year's worth of movement, and turning the quote into the range it prices over those three weeks is the step that makes the number usable at all.

Formula: expected move = spot x IV x sqrt(days / 365)

Your figures

Currency

Underlying price

Implied volatility

Annualised, as a percentage, taken from your own option chain.

Days to expiry

Counted on the basis chosen alongside.

Day count basis

Which calendar your volatility quote was built on. 365 spreads it over every day; 252 assumes price only moves when the market is open.

Results

Expected move

± US$8.60

one standard deviation, 8.60% of the price, over 30 days

One standard deviation range68.3% of outcomes finish inside it under a normal distribution.: US$91.40 to US$108.60
Two standard deviation move17.20% of the price — exactly twice the one sigma move.: ± US$17.20
Two standard deviation range95.4% of outcomes finish inside it under a normal distribution.: US$82.80 to US$117.20
At-the-money straddle this implies6.86% of the price, about four fifths of the one sigma move. Compare it with what the chain's own straddle costs.: US$6.86 per share
Time to expiry30 days over a 365-day year.: 0.0822 of a year

What this means

An annualised implied volatility of 30.00% spread over 30 days of a 365-day year works out at US$8.60 for one standard deviation, or 8.60% of the price. Under a normal distribution that places 68.3% of outcomes between US$91.40 and US$108.60, and 95.4% between US$82.80 and US$117.20. The same volatility prices an at-the-money straddle at roughly US$6.86 per share. These are the ranges the quoted volatility describes, not a forecast of where the price will go.

The range is arithmetic and symmetric about the price, whereas prices are closer to lognormal, so the real distribution is skewed with a longer right tail. The approximation holds well over short horizons at moderate volatility and degrades outside that.
The probabilities come from a normal distribution, which makes them model probabilities rather than forecasts. Real returns have fatter tails, so outcomes land outside these ranges rather more often than the figures suggest.
Every strike and expiry on a chain usually implies a different volatility. The answer is only as representative as the single quote entered here, which is yours to supply — nothing is fetched.
Volatility is rescaled by the square root of time because variance, not volatility, adds with time. Four times the horizon carries four times the variance and so twice the movement, which is why a weekly range is nowhere near a seventh of an annual one.

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Continue with these figures

About the Expected Move calculation

That conversion is not proportional, and assuming it is produces an answer far too small. Variance, not volatility, adds with time, so movement scales with the square root of the horizon: four times the days carries four times the variance and therefore twice the move. It is why the option implied range over a week is nowhere near a seventh of the one over a month, and why dividing an annual figure by twelve is wrong rather than merely rough.

The result is the standard deviation move options price over the days that remain, and it is the figure most option positions are ultimately measured against. A straddle's break-even distance, a strangle's move required past a strike, the width of a credit spread — each of them is a distance, and a distance means nothing until it is compared with the movement the market is pricing over the same number of days.

Used as an implied move calculator it takes an underlying price, an annualised implied volatility and a number of days, and returns the one and two standard deviation moves in points and as percentages, the ranges they describe, the model probability of finishing inside each, and the at-the-money straddle premium that the same volatility implies. Every input is yours — nothing is fetched, and no chain is read on your behalf.

Expected Move formula

basis         = 365 calendar days or 252 trading days
year fraction = days to expiry ÷ basis

one sigma move = spot × IV × √(year fraction)
two sigma move = 2 × one sigma move

range = spot ± sigma move          (lower bound floored at zero)

P(inside one sigma) = 2 × N(1) − 1 = 68.27%
P(inside two sigma) = 2 × N(2) − 1 = 95.45%

at-the-money straddle ≈ √(2/π) × one sigma move
                      ≈ 0.7979 × one sigma move

IV: Annualised implied volatility, entered as a percentage and used as a decimal — 30 becomes 0.30.
basis: Days in the year the quote is spread over: 365 counts every day, 252 counts only sessions.
N(x): Cumulative standard normal distribution — the probability of a draw falling below x.
√(2/π): 0.7979, the mean absolute value of a standard normal draw, and so the ratio of a straddle to one standard deviation.
year fraction: The option's remaining life as a share of a year on the chosen basis. 30 calendar days is 0.0822.

The square root is the whole of the rescaling and it is worth understanding rather than memorising. Successive returns are assumed independent, and independent variances add — so over n periods the variance is n times a single period's, and the standard deviation, being its square root, is √n times as large. Volatility is quoted as a standard deviation, which is why it grows with √time and not with time. The practical consequence is that short-dated options price a far larger fraction of the annual range than their length suggests, and long-dated ones a far smaller one.

The choice of basis matters more than it looks, and it is offered as an input because there is no universally right answer. Dividing by 252 rather than 365 assumes price only moves while the market is open, which produces a move about 20% larger for the same quote — √(365 ÷ 252) is 1.20. News does arrive at weekends, but most price discovery happens in session, so both conventions are defensible. What is not defensible is mixing them: a volatility built on one basis and spread over the other is simply the wrong number.

The 0.7979 in the straddle line is not a fudge factor. With rates and dividends at zero, an at-the-money straddle is worth 2 × S × (2 × N(σ√T ÷ 2) − 1), and expanding that to first order gives 2 × φ(0) × S × σ√T, which is √(2/π) × S × σ√T. The expansion is used rather than the closed form deliberately: 2 × N(x) − 1 subtracts two nearly equal numbers, so at the small σ√T of a short-dated option it loses most of its significant digits. The ratio form is exact at zero volatility, monotonic throughout, and happens to be the rule of thumb the market already quotes — the straddle is about four fifths of a one standard deviation move.

That same constant has a second meaning worth carrying away. √(2/π) × σ√T is the expected absolute move under a normal distribution — the average distance travelled, ignoring sign. So the straddle premium is not an approximation to the standard deviation at all; it is the mathematical expectation of the move, and the one sigma figure is the larger, more conservative band around it. When two sources disagree about what "the expected move" is, this is usually the disagreement.

Two simplifications are built in and neither is hidden. The range is arithmetic and symmetric about the current price, whereas real prices are closer to lognormal, so the true distribution is skewed with a longer right tail — an approximation that holds well over short horizons at moderate volatility and degrades outside that. And the probabilities are computed from the normal distribution rather than written in as 68 and 95, so the figures and the distribution they come from cannot drift apart; but they remain model probabilities, and real returns have fatter tails than the model allows.

Expected Move: a worked example

An underlying at 100 with an implied volatility of 30%, 30 calendar days to expiry, spread over a 365-day year.

Year fraction30 ÷ 365 = 0.0822
Square root of time√0.0822 = 0.2867
One sigma move100 × 0.30 × 0.2867 = 8.60
One sigma range100 ± 8.60 = 91.40 to 108.60
Two sigma move8.60 × 2 = 17.20
Two sigma range100 ± 17.20 = 82.80 to 117.20
Probability inside one sigma2 × N(1) − 1 = 68.27%
Implied straddle8.60 × 0.7979 = 6.86 per share

A move of ±8.60, which is 8.60% of the price, with 68.27% of outcomes inside 91.40 to 108.60 and 95.45% inside 82.80 to 117.20 under a normal distribution. The same volatility prices the at-the-money straddle at about 6.86 per share, so a chain quoting that straddle at 7.50 is carrying rather more volatility than the 30% entered here.

How to use the Expected Move calculator

Enter the current price of the underlying. Every output is scaled by it, so the ranges come back in the underlying's own units rather than as percentages alone.
Enter the annualised implied volatility from your own chain. The at-the-money figure for the expiry in question is the usual choice, since the calculation assumes one volatility across the whole range.
Enter the days to expiry and pick the basis your quote was built on: 365 spreads the volatility across every day, 252 assumes price only moves in session.
Read the one standard deviation range first. It is the band roughly two outcomes in three finish inside, under the model's assumptions rather than as a forecast.
Compare the implied straddle figure with what the at-the-money straddle actually costs on your chain. A larger quoted price means the market is pricing more movement than the volatility entered here.
Use the same number of days when setting this against a straddle or strangle's break-even distance. Two figures measured over different horizons are not comparable, however similar they look.

Limitations of the Expected Move calculator

Every calculation makes assumptions. These are the ones that matter here.

The range is arithmetic and symmetric about the current price, whereas prices are closer to lognormal. The real distribution is skewed with a longer right tail, and the gap widens as volatility and horizon grow.
The probabilities come from a normal distribution and are model probabilities, not forecasts. Real returns have fatter tails, so outcomes land outside these bands rather more often than 31.7% and 4.6% of the time.
Uses a single implied volatility for the whole calculation. Every strike and expiry on a chain implies its own, and the skew across strikes is precisely the market disagreeing with the constant-volatility assumption behind this arithmetic.
Assumes no drift. The range is centred on the current price rather than on the forward, so interest rates, dividends and cost of carry are all excluded — a difference that is negligible over weeks and real over years.
A lower bound below zero is reported as zero. That is not a repaired answer but the arithmetic announcing that a symmetric approximation has been stretched past the range where it means anything.
Says nothing about the path taken. A move that happens and then reverses before expiry leaves the underlying inside the range, which matters a great deal to any position closed before expiry.
Spreads volatility evenly across the days entered. A known event concentrates movement into a single session, so the day-by-day range this implies is not how the risk is actually distributed.

Frequently asked questions about Expected Move

What does the expected move actually mean?

It is the distance the quoted implied volatility prices over the days entered, expressed as one standard deviation. Under the model's assumptions roughly two outcomes in three finish within that band of the current price. It describes the range being priced, not a prediction of where the price will end up.

Should I use 365 or 252 days?

Whichever basis the volatility quote itself was built on. Most option pricing conventions use calendar days, so 365 is the common default; 252 assumes price only moves while the market is open and returns a move about 20% larger for the same quote. Mixing the two is the error worth avoiding.

Why is the at-the-money straddle only about 80% of the one sigma move?

Because √(2/π), or 0.7979, is the mean absolute value of a standard normal draw. The straddle pays the distance travelled regardless of direction, so its fair value is the expected absolute move — which is smaller than one standard deviation, since the standard deviation is a root-mean-square and gives more weight to large moves.

Is the 68% figure a real probability?

It is a model probability computed from the normal distribution, which is not the distribution real returns follow. Actual returns have fatter tails and more downside jumps, so outcomes fall outside the one sigma band more often than 31.7% of the time in practice. Treat it as the model's own accounting, not as a measured frequency.

Why doesn't this match the straddle price on my chain?

Usually because the chain is pricing a different volatility than the one entered. The implied straddle figure is derived from a single quote; the market's own straddle reflects the actual at-the-money implied volatility, plus the bid-ask spread, any early-exercise value and the skew between the call and the put strikes.

Can this be used for an earnings expected move?

It can be used to read the range priced into the expiry that contains the event, by entering the implied volatility of that expiry. What it cannot do is separate the event from the ordinary days around it — the calculation spreads volatility evenly, whereas an event concentrates most of it into one session.

Last reviewed 29 August 2026. See our methodology and editorial policy.

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