Ict Standard Deviation Calculator
Calculate standard deviation projections from Asian range for ICT daily range expansion. Enter values for instant results with step-by-step formulas.
Calculator
Adjust values & calculateBullish SD Projection Levels
Formula
Where SD Level is the projected price target, Asian High is used for bullish projections (or Asian Low for bearish), Asian Range is the difference between Asian session high and low, and SD Multiplier ranges from 1.0 to 4.0.
Last reviewed: December 2025
Worked Examples
Example 1: EUR/USD Bullish SD Projections from Asian Range
Example 2: GBP/USD Bearish SD Expansion Analysis
Background & Theory
The Ict Standard Deviation Calculator applies the following established principles and formulas. Statistics and probability provide the mathematical framework for drawing conclusions from data under uncertainty. The measures of central tendency describe where data cluster. The mean is the arithmetic average, computed as the sum of all values divided by the count. The median is the middle value of an ordered dataset, robust to extreme outliers. The mode is the most frequent value. Spread is quantified by variance, the average squared deviation from the mean, and by its square root, the standard deviation. For a sample, variance uses n minus one in the denominator to correct for bias in estimation. The normal distribution, defined by its mean and standard deviation, is the cornerstone of parametric statistics. Its bell-shaped probability density follows the formula f(x) = (1 / (sigma * sqrt(2*pi))) * exp(-0.5 * ((x - mu) / sigma)^2). The empirical rule states that approximately 68 percent of observations fall within one standard deviation of the mean, 95 percent within two, and 99.7 percent within three. A z-score standardizes a data point by subtracting the mean and dividing by the standard deviation, expressing how many standard deviations an observation lies from the mean. In hypothesis testing, the p-value is the probability of observing a result at least as extreme as the one obtained, assuming the null hypothesis is true. Confidence intervals express the range within which the true population parameter falls with a specified probability, typically 95 percent. Correlation measures linear association between two variables, with Pearson's r ranging from negative one to positive one. Correlation does not imply causation. Linear regression fits a line of the form y = a + bx to minimize the sum of squared residuals. Bayes' theorem relates conditional probabilities: P(A|B) = P(B|A) * P(A) / P(B), allowing prior beliefs to be updated on new evidence. The law of large numbers guarantees that the sample mean converges to the population mean as sample size grows. The central limit theorem states that the distribution of sample means approaches normality regardless of the population distribution, provided the sample size is sufficiently large, typically 30 or more.
History
The history behind the Ict Standard Deviation Calculator traces back through the following developments. The mathematical study of probability emerged in the 17th century from correspondence between Blaise Pascal and Pierre de Fermat in 1654. Their exchange, prompted by a gambling problem posed by the Chevalier de Mere, established the foundations of probability theory by calculating expected outcomes through systematic enumeration of cases. Jacob Bernoulli formalized the law of large numbers in his posthumously published Ars Conjectandi of 1713, proving rigorously that empirical frequencies converge to theoretical probabilities with increasing observations. His work laid the groundwork for inferential statistics by connecting mathematical probability to observed data. Carl Friedrich Gauss developed the method of least squares around 1795 while adjusting astronomical observations, and he recognized the bell-shaped error distribution that now bears his name. Pierre-Simon Laplace independently worked on the normal distribution and proved an early version of the central limit theorem around 1810, demonstrating why errors in measurement tend toward normality. The late 19th century saw statistics emerge as a distinct scientific discipline. Francis Galton introduced regression and correlation in the 1880s while studying heredity. Karl Pearson formalized these concepts, developed the chi-squared test, and founded the journal Biometrika in 1901, establishing statistics as a rigorous academic field. Ronald Fisher transformed statistical practice in the early 20th century. His 1925 book Statistical Methods for Research Workers introduced significance testing, analysis of variance, and the concept of the p-value as a decision threshold, establishing the framework still used in scientific research. Fisher and Jerzy Neyman engaged in a prolonged methodological dispute over the interpretation of hypothesis tests. The Bayesian approach, rooted in the 18th century work of Thomas Bayes and Laplace, was largely eclipsed by frequentist methods through much of the 20th century but experienced a revival after World War II and accelerated with computational advances. The late 20th and early 21st centuries brought statistics into every domain through big data, machine learning, and the routine availability of software capable of processing millions of observations.
Key Features
- Computes a full descriptive statistics summary from a data set, including mean, median, mode, range, variance, standard deviation, skewness, and interquartile range.
- Constructs confidence intervals for population proportions and means at any confidence level, displaying the margin of error, standard error, and critical value used.
- Calculates p-values and test statistics for z-tests, one- and two-sample t-tests, and chi-square goodness-of-fit and independence tests, with automatic two-tailed or one-tailed selection.
- Performs ordinary least squares linear regression on paired data, returning the slope, intercept, R-squared value, and a residual summary to assess model fit.
- Evaluates the CDF and PDF for major probability distributions including the normal, binomial, and Poisson distributions, given user-supplied parameters and input values.
- Determines the required sample size to achieve a specified margin of error and confidence level for both proportion and mean estimation problems.
- Computes the Pearson and Spearman correlation coefficients between two variables, indicating the strength and direction of their linear or monotonic relationship.
- Applies Bayes' theorem to calculate posterior probabilities given a prior probability, likelihood, and marginal likelihood, with a clear breakdown of each term in the formula.
Frequently Asked Questions
Formula
SD Level = Asian High/Low + (Asian Range x SD Multiplier)
Where SD Level is the projected price target, Asian High is used for bullish projections (or Asian Low for bearish), Asian Range is the difference between Asian session high and low, and SD Multiplier ranges from 1.0 to 4.0.
Worked Examples
Example 1: EUR/USD Bullish SD Projections from Asian Range
Problem: EUR/USD Asian range is 1.0980-1.1020 (40 pips). ADR is 80 pips. Bias is bullish. Calculate all SD projection levels.
Solution: Asian range: 40 pips (1.0980 - 1.1020)\n1.0 SD from Asian high: 1.1020 + 0.0040 = 1.1060\n2.0 SD: 1.1020 + 0.0080 = 1.1100\n2.5 SD: 1.1020 + 0.0100 = 1.1120\n3.0 SD: 1.1020 + 0.0120 = 1.1140\n4.0 SD: 1.1020 + 0.0160 = 1.1180\nADR comparison: 2.0 SD (80 pips total from low) matches ADR\nOptimal target: SD 2.0-2.5
Result: SD 2.0: 1.1100 | SD 2.5: 1.1120 | SD 3.0: 1.1140 | Optimal: SD 2.0
Example 2: GBP/USD Bearish SD Expansion Analysis
Problem: GBP/USD Asian range 1.2750-1.2780 (30 pips). Price dropped to 1.2710. ADR is 100 pips. Calculate current expansion and remaining targets.
Solution: Asian range: 30 pips\nCurrent expansion from Asian low: 1.2750 - 1.2710 = 40 pips = 1.33 SD\nSD 2.0 target: 1.2750 - 0.0060 = 1.2690 (40 pips away)\nSD 2.5 target: 1.2750 - 0.0075 = 1.2675 (35 pips further)\nSD 3.0 target: 1.2750 - 0.0090 = 1.2660\nADR suggests room for SD 3.0+ (only 70/100 pips used)\nOptimal target: SD 3.0
Result: Currently at 1.33 SD | SD 2.0: 1.2690 | SD 3.0: 1.2660 | 40 pips remaining to SD 2.0
Frequently Asked Questions
What is the ICT Standard Deviation projection and how is it calculated?
The ICT Standard Deviation projection is a method for forecasting potential daily price targets based on the width of the Asian trading session range. The concept uses the Asian range as one unit of standard deviation (1 SD) and then projects multiples of this range from the Asian session high or low to identify potential expansion targets. For example, if the Asian range is 40 pips, the 1 SD projection is 40 pips beyond the Asian high (bullish) or low (bearish), the 2 SD projection is 80 pips, 2.5 SD is 100 pips, and so on. ICT teaches that the typical daily range expansion reaches between 2.0 and 3.0 standard deviations from the Asian range, with the most common target being the 2.5 SD level.
Why is the Asian session range used as the basis for standard deviation calculations?
The Asian session range is used because it represents the accumulation phase of the daily Power of Three cycle, where institutional algorithms establish their positions within a defined range before expanding price during the London and New York sessions. The width of this accumulation range reflects the current market conditions, with tighter ranges indicating potential for larger expansions and wider ranges suggesting the market may have already priced in significant movement. The Asian range also acts as a natural volatility measure specific to each trading day, unlike fixed pip targets that do not account for changing market conditions. By using the Asian range as the SD unit, the projection automatically scales with daily volatility.
What are the typical probability levels for each standard deviation projection?
Based on ICT observations and historical analysis, the probability of price reaching each standard deviation level decreases as the projection extends further. The 1.0 SD level is reached approximately 75 percent of trading days, as most sessions feature at least a moderate expansion beyond the Asian range. The 2.0 SD level is reached about 50 percent of the time, representing an average daily expansion. The 2.5 SD level, which is the most commonly referenced target, is reached approximately 35 percent of the time on trending days. The 3.0 SD level represents significant expansion reached about 20 percent of the time, typically on high-volatility days. The 4.0 SD level is an extreme expansion reached only about 10 percent of the time, usually coinciding with major news events or trend days.
How does the Average Daily Range relate to standard deviation projections?
The Average Daily Range (ADR) provides an independent benchmark for validating standard deviation projections. If the ADR is 80 pips and the Asian range is 30 pips, then the expected daily expansion would be approximately 2.5 to 3.0 standard deviations (75-90 pips from the Asian low to the daily high). When the SD projection aligns with the ADR, it increases confidence in the target level. If the 2.5 SD projection exceeds the ADR significantly, it suggests the target may be too ambitious for a normal day. Conversely, if the 2.0 SD projection is well below the ADR, a wider expansion toward 3.0 or 4.0 SD becomes more likely. Ict Standard Deviation Calculator compares your SD projections against the ADR to recommend the optimal target level.
When should I use bullish versus bearish standard deviation projections?
The direction of standard deviation projections should align with your higher timeframe institutional bias and the Power of Three (AMD) analysis for the current day. Use bullish projections when the daily or 4-hour chart shows bullish market structure (higher highs and higher lows), when price has swept sell-side liquidity below the Asian low during the London session manipulation phase, and when the seasonal tendency supports upward movement. Use bearish projections when market structure is bearish, when buy-side liquidity above the Asian high has been swept, and when the overall bias is down. The direction is typically confirmed during the London session when the manipulation phase reveals which side of the Asian range the algorithm targets for the initial liquidity sweep.
What is the optimal standard deviation level to use as a profit target?
The optimal SD level for profit targets depends on market conditions and the specific day type. For average volatility days, the 2.0 SD level provides a realistic target with a 50 percent probability of being reached. For trending days with clear directional momentum and multiple confluences, the 2.5 SD level offers a good balance between probability and reward. On high-impact news days or days following prolonged consolidation, the 3.0 SD level becomes viable as breakout energy drives extended expansion. A practical approach is to take partial profits at the 2.0 SD level (50 percent of position) and trail the remainder toward the 2.5 or 3.0 SD level. This ensures some profit is captured while allowing for full daily expansion when it occurs.
References
Reviewed by Daniel Agrici, Founder & Lead Developer · Editorial policy