Mathematical Calculators

Empirical Rule Calculator

The empirical rule calculator, also known as a "68 95 99 rule calculation", is a tool that allows you to determine the ranges that are either 1 or 2 standard deviations or 3 standard deviations. This calculator will show you the ranges in which 68, 95, or 99.7% of normally distributed data, respectively.

Empirical Rule Calculator

68% of data falls between
? and ?
95% of data falls between
? and ?
99.7% of data falls between
? and ?
made with ❤️ by

Table of contents

What is the empirical rule?
Where is the empirical rule applied?
How does the Empirical Rule work?
What are the Benefits Of The Empirical Rule?

What is the empirical rule?

The empirical rule, also known as the three-sigma or the 68–95-99.7 rules, is a statistical rule that states that almost all data for normally distributed data will fall within three standard deviations.
You'll also find:
  • 68% data within 1 standard deviation
  • 95% data within 2 standard deviations
  • 99.7% data within 3 standard deviations
  • The standard deviation shows the spread of the data. It tells how different the data is from the average. The narrower the data range, the smaller the value.
    A normal distribution refers to a distribution that is symmetric around the mean. Data near the mean are more common than data farther from the mean. Normal distributions look like a bell-shaped curves in graphical form.

    Where is the empirical rule applied?

    This rule is used extensively in empirical research. It can be used to calculate the probability that a particular piece of data will occur or to forecast outcomes when not all data are available. It provides insight into the characteristics and distribution of a population, without having to test everyone. It can also be used to identify outliers, which are results that are significantly different from the rest of the data set. These may be due to experimental errors.

    How does the Empirical Rule work?

    The empirical rule can be used to predict probable outcomes in normal distributions. An example of this would be used by a statistician to determine the percentage that falls within each standard deviation. Consider the following: The standard deviation of 3.1 is equal to 10. The first standard deviation in this example would range from (10+3.22)= 13.2 to (10-3.22)= 6.8. The second standard deviation would be between 10 + (X 3.2 = 16.4 and 10-(X 3.2 = 3.6), and so on.

    What are the Benefits Of The Empirical Rule?

    The empirical rule works well because it is a way to forecast data. This is especially true with large datasets, and variables that are not known. This is especially true in finance. It applies to stock prices and price indices. Log values of forex rates are also relevant. They all tend towards a bell curve or normal distribution.
    John Cruz
    Article author
    John Cruz
    John is a PhD student with a passion to mathematics and education. In his freetime John likes to go hiking and bicycling.
    Empirical Rule Calculator English
    Published: Thu Jul 21 2022
    In category Mathematical calculators
    Add Empirical Rule Calculator to your own website

    Other mathematical calculators

    Vector Cross Product Calculator

    Vector cross product calculator finds the cross product of two vectors in a three-dimensional space.

    30 60 90 Triangle Calculator

    With our 30 60 90 triangle calculator you can solve the special right triangle.

    Expected Value Calculator

    This expected value calculator helps you to calculate an expected value (also called ​mean) of the given variable set with their probabilities.

    Online Scientific Calculator

    This scientific calculator provides simple and advanced mathematical functions in an easy-to-use app.

    Standard Deviation Calculator

    This free calculator gives you the standard deviation, variance, mean, and sum of a given data set.

    Percentage Calculator

    This percentage calculator is a free online calculator to calculate percentages. Find out what is X % of Y?

    Fractions Calculator

    This free fraction calculator can be used to find the result for adding, subtracting, multiplying, and dividing two common fractions.

    Pounds To Cups Converter: Flour, Sugar, Milk..

    Find out correct measurements for your favourite recipe with this free calculator converts pounds to cups easily! Works with US cups and UK cups!

    Circle Circumference Calculator

    Use this free circle circumference calculator to calculate circle radius, circle diameter, circle circumference, and circle area.

    Double Angle Formula Calculator

    Determine the double angle equivalent of a given angle with this free calculator! Find more information about the double angle formula.

    Mathematical Root Calculator (square Root Calculator)

    This free calculator calculates the second, third and higher exponents and roots. Formula is also available.

    Triangle Area Calculator

    Find out area of triangle easily with our free triangle area calculator! You can calculate with base and height, three different sides and many more. Works with angles and radians!

    Coterminal Angle Calculator

    Find out coterminal angles with our coterminal angle calculator! Works with degrees and radians to find out positive and negative coterminal angles!

    Dot Product Calculator

    Calculate mathematical dot products, scalar products and dot product angles easily for your vectors.

    Midpoint Calculator

    Find out midpoints for a line or a triangle easily with our midpoint calculator! This page will also teach you valuable midpoint formula!

    Significant Figures Converter (Sig Figs Calculator)

    Find out the correct amount of significant figures in your number easily with our significant figure tool!

    Arc Length Calculator For Circle

    Find out easily length of a circle's arc with this online math calculator!

    Point Estimate Calculator

    Calculate point estimate easily with our free online tool!

    Percentage Increase Calculator

    Calculate any percentage increase easily with our free online calculator!

    Percentage Difference Calculator

    Calculate percentage difference instantly with our mathematical percentage difference calculator!

    Linear Interpolation Calculator

    This free online calculator calculates the linear interpolation and the linear extrapolation. It also provides the slope of the linear equation.

    QR Decomposition Calculator

    Find out orthonormal matrix and upper triangular matrix easily with our free online QR decomposition calculator!

    Matrix Transpose Calculator

    This matrix transpose calculator helps you to find a transpose for any matrix.

    Triangle Hypotenuse Calculator

    Find out hypotenuse for all kinds of triangles easily with our free math calculator!

    Trigonometry Calculator

    Calculate easily trigonometric values Sin, Cos, Tan, Cot, Sec and Csc with our free online calculator!

    Right Triangle Side And Angle Calculator (triangle Calculator)

    FInd out easily right side and angle of an triangle with our free online calculator!

    45 45 90 Triangle Calculator (right Triangle Calculator)

    Calculate hypotenuse, measurements and ratio easily with our 45 45 90 triangle calculator.

    Matrix Multiply Calculator

    Calculate matrix multiplications easily with our free online math calculator!

    Average Calculator

    Calculate mean average of numbers easily with our free online math calculator

    Random Number Generator

    This tool generates a truly random number between any two numbers.

    Margin Of Error Calculator

    This calculator calculates the margin of error for surveys based on sample size and proportion. It also allows you to set the desired level of confidence.

    Angle Between Two Vectors Calculator

    This online tool calculates the angle between two vectors and has all the possible vector combinations.

    LCM Calculator - Least Common Multiple Calculator

    This calculator will help you find the LCM or LCD for a particular set of numbers.

    Square Footage Calculator

    This online calculator calculates the area of a shape measured in feet. Works with all shapes and measurement units!

    Exponent Calculator (power Calculator)

    This is an online calculator that can calculate exponents.

    Math Remainder Calculator

    This online tool calculates the remainder of a division.

    Rule Of Three Calculator - Direct Proportion

    Calculate easily direct proportion of numbers with our free Rule of Three calculator.

    Quadratic Formula Calculator

    Quadratic equations are any polynomial algebra of the second degree having the following form in algebra.

    Sum Calculator

    This summation notation calculator allows you to quickly calculate the summation of a set number, also known as Sigma. Therefore it is often called a sigma calculator. It also gives you a sample from the series to be a sum. It can be used in simple mode to calculate a simple sum using a given set of numbers.

    Perimeter Calculator

    This is a free online tool that will calculator the perimeter of different shapes.

    Z Score Calculator (z Value)

    This is a calculator that calculates the z-score of a data set.

    Fibonacci Calculator

    This Fibonacci calculator can be used to calculate the terms arbitrarily of the Fibonacci sequence.

    Capsule Volume Calculator

    It is a free calculator that can help you find the volume of any capsule.

    Pyramid Volume Calculator

    It is a free calculator that can help you find the volume of different shapes.

    Triangular Prism Volume Calculator

    It is a free calculator that can help you find the volume of any triangular prism.

    Rectangle Volume Calculator

    It is a free calculator that can help you find the volume of a box.

    Cone Volume Calculator

    This calculator calculates cone volume and can be used to solve school problems.

    Cube Volume Calculator

    This is an online tool that will calculate the volume of any cube.

    Cylinder Volume Calculator

    This is an online tool that will calculate the volume of a cylinder.

    Scale Factor Dilation Calculator

    This is an online calculator that will help you calculate the scale factor dilation of an object.

    Shannon Diversity Index Calculator

    The Shannon biodiversity index calculator can be used to calculate the diversity of species in a community. Ecologists can use the Shannon diversity index to gain useful information about habitat.

    Bayes Theorem Calculator

    Use this Bayes theorem calculator online to determine the probability of an event that is conditional on another. This calculation takes into account the prior probability of A, the probabilities B conditional and A conditional, and A conditional.

    Antilogarithm Calculator

    The antilog calculator allows you to calculate the inverse logarithm function. Calculate the antilogarithm for any number with any base, whether it's 10, natural antilog, or another number.

    Eˣ Calculator

    This amazing tool will allow you to compute e to the power of any number you choose.

    Prime Number Calculator

    This calculator will show you whether a number has a prime number or if it is a composite.

    Exponential Growth Calculator

    The exponential Growth Calculator calculates the final price of a quantity based on its initial values, rate of growth, and time.

    Sample Size Calculator

    Calculate sample size based on the population size, confidence level, and margin of error.

    Inverse Logarithm (log) Calculator

    This online calculator will display the inverse log of the number and the base entered.

    Poisson Distribution Calculator

    The Poisson distribution calculator will allow you to determine the likelihood of an event occurring a number of times during a certain time frame.

    Multiplicative Inverse Calculator

    This calculator will help you find the multiplicative inverse of an integer, a decimal, a fraction, or a mixed number.

    Marks Percentage Calculator

    This calculator converts test marks to percentages. It can be used to quickly calculate the percentage of one or more test grades (marks), and the maximum number of marks.

    Ratio Calculator

    This calculator can be used to determine the dimensions of images when you resize them.

    P-value-calculator

    This incredible tool will allow you to find the p-value. You can use test statistics to determine which p-value is one-sided and which is two-sided.

    Sphere Volume Calculator

    It is a free calculator that can help you find the volume of a sphere.

    NPV Calculator

    This online calculator will allow you to calculate the NPV (Net Present Value) of an investment. The calculation is based on the initial investment and the discount rate. You can also calculate Internal Rates of Return (IRR), gross returns, and net cash flows.

    Percentage Decrease

    Use this calculator to find out how a percentage decrease by any amount will change the result. Simply enter the original value, the percentage decrease, and the new value to calculate the change.

    Area Calculator

    Our intuitive tool lets you choose from different shapes and calculates their area in the blink of an eye.

    Probability Calculator

    The probability calculator lets you explore the relationships of likelihood between two separate events. This allows you to get a better understanding of how events are related, and thereby makes predictions more accurate.

    Fraction To Decimal Calculator

    Use our fraction to decimal calculator to easily convert fractions to decimals and back again!

    Factor Calculator

    Find out the factors of any number with our factor calculator

    Fraction To Mixed Number Calculator

    Convert a fraction to a mixed number calculator using our simple tool