Calculator Error Propagation
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EXP, LNe, LOG, SIN, uncertainty calculator SQR, TAN. Variables are one or two characters, e.g. I, X, df, X7. Nested parentheses are useful, e.g. ((X+Y)*Z). No implicit multiplication,
Error Propagation Equation
e.g. ((X+Y)Z) is not allowed. Variables are not case sensitive: x=X. Scientific notation: 1.23x10-3 is written as 1.23E-3. Enter your equation without an "=" sign. -----Example: ----- To evaluate K2, knowing K1, H, R, T2,and T1 in the equation: ln(K2/K1) = - H/R( 1/T2 - 1/T1) Solve for K2. You would then enter Equation: K1*EXP(-H/R*(1/T2-1/T1)) Equation: Result= Colby College Chemistry, T. W. Shattuck
Be sure to precede decimal points with a zero. For example, use "0.01", never ".01". Enter parameters X value ±dX Operator Y value ±dY + − × ÷ ln log
Propagation Of Error Multiplication
e^y 10^y x^a Preview your expression Z = (X±dX) + (Y±dY) error propagation example Result Z value ±dZ Memory ± What is this good for? Imagine you derive a new propagation of error addition parameter (using various mathematical operations) from an existing one with a given standard deviation, and need to know what the standard deviation of that new parameter is. http://www.colby.edu/chemistry/PChem/scripts/error.html?ModPagespeed=off In other words, you want to know how the standard deviation of the primary parameter(s) propagates to the resulting parameter. This calculator simplifies the calculus by making the most common operations automatically. Instructions Enter numbers in correct format "Scientific" format is acceptable (the maximum exponent = 99 as in regular calculators). Examples: 0.001 https://www.eoas.ubc.ca/courses/eosc252/error-propagation-calculator-fj.htm can be also entered as 1e-3 or 1E-3 or 1e-03 or 1E-03 or 10e-4 and so on 325 can be also entered as 3.25e2 or 3.25e+2 or 3.25e+02 and so on Standard deviation by definition must be a non-negative number (i.e. it is zero or positive) Enter all numbers required for given operation. Standard deviations are not required at all; if they are not entered, the calculator will perform the requested operation, but no error propagation calculation Division requires a divisor other than zero Logarithms require positive arguments Incorrect or missing required numbers are highlighted Results can be saved into memory and recalled later in the subsequent calculations. To save your result, use the "Z→M" button. To recall saved numbers (both the value and error), click "MR→X" or "MR→Y". Further reading Uncertainties and Error Propagation Treatment of errors by Steve Marsden Except where otherwise noted, this work is licensed under a Creative Commons License. © 2005-2008 richard laffers
Random Entry New in MathWorld MathWorld Classroom About MathWorld Contribute to MathWorld Send a Message to the Team MathWorld Book Wolfram Web Resources» 13,594 entries Last updated: Tue Sep 27 http://mathworld.wolfram.com/ErrorPropagation.html 2016 Created, developed, and nurturedbyEricWeisstein at WolframResearch Probability and Statistics>Error Analysis> Interactive Entries>Interactive Demonstrations> Error Propagation Given a formula with an absolute error in of , the absolute error is . The relative error is . If , then (1) where denotes the mean, so the sample variance is given by (2) (3) The definitions of variance error propagation and covariance then give (4) (5) (6) (where ), so (7) If and are uncorrelated, then so (8) Now consider addition of quantities with errors. For , and , so (9) For division of quantities with , and , so (10) Dividing through by and rearranging then gives (11) For exponentiation of quantities with (12) and propagation of error (13) so (14) (15) If , then (16) For logarithms of quantities with , , so (17) (18) For multiplication with , and , so (19) (20) (21) For powers, with , , so (22) (23) SEE ALSO: Absolute Error, Accuracy, Covariance, Percentage Error, Precision, Relative Error, Significant Digits, Variance REFERENCES: Abramowitz, M. and Stegun, I.A. (Eds.). Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover, p.14, 1972. Bevington, P.R. Data Reduction and Error Analysis for the Physical Sciences. New York: McGraw-Hill, pp.58-64, 1969. Referenced on Wolfram|Alpha: Error Propagation CITE THIS AS: Weisstein, Eric W. "Error Propagation." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/ErrorPropagation.html Wolfram Web Resources Mathematica» The #1 tool for creating Demonstrations and anything technical. Wolfram|Alpha» Explore anything with the first computational knowledge engine. Wolfram Demonstrations Project» Explore thousands of free applications across science, mathematics, engineering, technology, business, art, finance, social sciences, and more. Computerbasedmath.org» Join the initiative for modernizing math education. Online Integral Calculator» Solve integrals with Wolfram|Alpha. Step-by-step S