Volatility converter

Rescale a volatility between horizons using the square-root-of-time rule, and see every conversion at once.

Quick answer: The volatility converter rescales a volatility figure between horizons using the square-root-of-time rule: to move from one period to another, multiply by the square root of the ratio of their lengths. Doubling the horizon multiplies volatility by 1.41, not by 2.

Volatility Converter

Enter any one volatility and its horizon; the calculator shows the equivalent at every other horizon.

Figures are per unit of the underlying and exclude brokerage, STT, exchange charges, stamp duty and GST.

How this calculator works

Why the square root, and not the ratio

Under independent returns, VARIANCE scales linearly with time: two days have twice the variance of one. Volatility is the square root of variance, so it scales with the square root of time. Doubling the horizon multiplies expected dispersion by √2 ≈ 1.41, not by 2. This single fact is the reason a month's volatility is not four times a week's, the reason vega scales with √T, and the reason forward volatility exceeds the spot volatility that spans it.

The rule that everyone remembers

An annualised volatility divided by √252 ≈ 15.87 gives the typical daily move. India VIX at 13 therefore implies a typical NIFTY day of about 13 ÷ 15.87 ≈ 0.82%. Traders round √252 to 16 and do this in their heads. It is the most useful piece of arithmetic in the whole subject.

252, 365, and the deliberate inconsistency

Volatility is annualised on 252 trading days, because a closed market does not move. Time to expiry inside a pricing formula is calendar days ÷ 365, because interest accrues on weekends. These conventions contradict each other, both are universal, and the contradiction is the single most common reason a reader's spreadsheet disagrees with a broker's screen by a percent or two.

Where the rule breaks

The √t rule assumes returns are independent across periods. They are not. In a trending market returns are positively autocorrelated, so multi-period dispersion EXCEEDS what the rule predicts and a scaled daily volatility understates the real risk. In a range-bound market returns are negatively autocorrelated and it overstates it. The rule is at its least reliable in precisely the regimes people most want to use it in.

The square-root-of-time rule

σ_target = σ_source × √( periods_source ÷ periods_target )

Where 'periods' counts how many of that horizon fit in a year: 252 daily, 52 weekly, 12 monthly, 1 annual. Equivalently: annualise by multiplying by √(periods per year), de-annualise by dividing.

σ_sourceThe volatility you have, expressed over its own horizon.
σ_targetThe volatility you want, expressed over the target horizon.
periods_sourceHow many source-horizon periods fit in one year (252 for daily, 52 weekly, 12 monthly, 1 annual).
periods_targetHow many target-horizon periods fit in one year.

Using it, step by step

Enter the volatility figure you have and select the horizon it is quoted over. An implied volatility from an option chain is always annualised.
Optionally enter a spot price to see the equivalent move in points or rupees.
Read the equivalent volatility at every other horizon.
Sanity-check with the mental shortcut: annualised volatility divided by 16 is roughly the daily move in percent.
Remember that the target figure is a standard deviation, not a maximum. About one day in three exceeds the daily figure.

Worked example

NIFTY

India VIX reads 13, meaning a 13% annualised expected volatility for NIFTY over the next 30 days. Divide by √252 = 15.87 to get a typical daily move of 0.82%, which on a spot of 24,000 is about 197 points. Scale to a week (5 trading days) by multiplying by √5: 0.82% × 2.236 = 1.83%, or about 440 points. Note that the 7-calendar-day expected move computed the option-pricing way — 24,000 × 0.13 × √(7/365) — gives 432 points. The two differ because one counts 5 trading days and the other 7 calendar days. Neither is wrong; they are answering slightly different questions, and knowing which you asked is most of the skill.

Assumptions and limitations

What this calculator assumes. Every number it produces is only as good as the assumptions below, and each of them is wrong to some degree in a real market. The output is a model's opinion, not a measurement.

Returns are independent across periods. This is what licenses the square root, and it is false: volatility clusters, and returns are autocorrelated in trending and range-bound markets.
The volatility is constant over the horizon being scaled. Over any horizon long enough to matter, it is not — volatility mean-reverts.
252 trading days per year is a convention; NSE trades roughly 250 depending on holidays. The effect on the answer is under half a percent.
Scaling a daily volatility to an annual one assumes no overnight gaps that behave differently from intraday movement. In practice, gap risk has its own distribution and this rescaling blends the two.
The result is a standard deviation, not a bound. Roughly one period in three exceeds it, and fat tails mean the extremes exceed it by more than the normal model allows.

Common mistakes

Scaling by the ratio of periods rather than its square root — multiplying a daily volatility by 252 instead of √252, and getting an answer sixteen times too large.
Annualising with √365 instead of √252, overstating volatility by about 20%.
Mixing conventions inside one calculation: annualising realised volatility on 252 days and then computing an expected move with the same figure over calendar days, without noticing the inconsistency.
Applying the rule across a regime change, where returns are strongly autocorrelated and the square root is simply the wrong function.
Reading a scaled figure as a maximum move rather than a one-standard-deviation move.

Frequently asked questions

How do I convert annualised volatility to a daily move?

Divide by the square root of 252, which is about 15.87. An annualised volatility of 13% implies a typical daily move of about 0.82%.

Why is volatility scaled by the square root of time?

Because variance scales linearly with time under independent returns, and volatility is the square root of variance. Two days have twice the variance of one day, so √2 times the volatility.

How do I convert a daily volatility to annual?

Multiply by the square root of 252. A daily standard deviation of 0.85% annualises to 0.85% × 15.87 ≈ 13.5%.

Should I use 252 or 365 days?

Use 252 for annualising volatility, because a closed market does not move. Use 365 for the time-to-expiry input of a pricing formula, because interest accrues on weekends. Both conventions are standard and they contradict each other.

Does the square-root-of-time rule always work?

No. It assumes returns are independent across periods. In a trending market returns are positively autocorrelated and the rule understates multi-period dispersion; in a range-bound market it overstates it.

How do I convert India VIX into an expected weekly move?

Divide India VIX by 15.87 to get the daily move, then multiply by √5 for a five-trading-day week. At VIX 13 that is 0.82% × 2.236 ≈ 1.83%, about 440 NIFTY points from 24,000.

Is a monthly volatility four times a weekly one?

No — it is about twice. A month is roughly four weeks, and √4 = 2. This is the most common arithmetic error in the whole subject.

Does this converter work for BANKNIFTY?

Yes. The scaling rule is a property of the arithmetic, not of the underlying. Enter BANKNIFTY's spot to see the moves in points.

Voice search & related questions

How do I convert VIX to a daily move?

Divide the VIX level by about 16, which is the square root of 252. A VIX of 13 implies a typical daily move of roughly 0.8%.

Why isn't monthly volatility four times weekly volatility?

Because volatility scales with the square root of time, not with time. A month is about four weeks, and the square root of four is two, so monthly volatility is roughly double weekly volatility.

What is the square root of time rule?

It says that to rescale a volatility from one horizon to another, you multiply by the square root of the ratio of the horizons. It follows from the fact that variance, not volatility, adds across independent periods.

Last reviewed 10 July 2026. Educational content only — not investment advice.