laffers.net

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Enter parameters

X value
±dX
Operator
Y value
±dY

+−×÷lnloge^y10^yx^a

Preview your expression

Z = (X±dX) + (Y±dY)

Result

Z value
±dZ

Memory

±

What does it do?

Whenever you calculate a new parameter (using various mathematical operations) from other parameters with given standard deviations, you may want to know the standard deviation of that new parameter. 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 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”.

Other tools

• Lab Statistics – Windows-based program performing the above and other statistical math in an efficient way
• EPC Error-propagation calculator – an error-propagating calculator, with Perl-like syntax for Linux
• Fussy: Automatic Error Propagation – a programable scientific calculator with a scripting languge for automatic random error propagation in arbitrary mathematical expressions (Linux OS only). The language allows expressions written as a collection of sub-expressions or user defined functions.
• Uncertainty Calculator – another online calculator

Further reading

• Uncertainties and Error Propagation
• Treatment of errors by Steve Marsden

Tags: science

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