This tool helps you to determine the uncertainty (or error) of any mathematical expression that contains physical quantities with uncertainties. It follows the rules of the Gaussian error propagation: If f is a function of the independent variables X and Y, written as f(X,Y), then the uncertainty in f is obtained by taking the partial derivatives of f with respect to each variable, multiplication with the uncertainty in that variable, and addition of these individual terms in quadrature.
Use "." as decimal mark: 1.234, not 1,234.
How to use
- Enter a valid formula using the functions listed at the bottom.
- In the "quantities with errors" section define all variables which appear in your formula. Use "." as decimal mark, not ",".
- Hit evaluate and get the result along with its absolute and relative uncertainty.
Example
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Formula: log(a)+(b*pow(c,2))*sin(c) with variables a, b, c Exact error (calculated analytically): 56.88139881918965 Error calculated by this tool (numerically): 56.882447776373766
Deviation: |
Notes
Keep in mind that this tool carries out numerical calculations which do not have the same value as analytical methods. However, in all known cases the deviations between numerical and analytical results were negligibly small.
Do not use the symbols "^" or "**" to express "raised to the power of". There is the "pow(x,y)" function instead. The following math methods are available and can be used in the formula field:
| Method | Description |
|---|---|
| acos(x) | Returns the arccosine of x, in radians |
| asin(x) | Returns the arcsine of x, in radians |
| atan(x) | Returns the arctangent of x as a numeric value between -PI/2 and PI/2 radians |
| cos(x) | Returns the cosine of x (x is in radians) |
| exp(x) | Returns the value of Ex |
| log(x) | Returns the natural logarithm (base E) of x |
| pow(x,y) | Returns the value of x to the power of y |
| sin(x) | Returns the sine of x (x is in radians) |
| sqrt(x) | Returns the square root of x |
| tan(x) | Returns the tangent of an angle |
Furthermore Euler's constant and Pi are represented by "E" and PI" respectively.
