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 of this page.
- In the "quantities with errors" section define all variables which appear in your formula. Use "." as decimal mark, not ",".
- Click "Evaluate" to obtain 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
This tool is based on numerical methods. However, even for complicated formulas the deviation between numerical and analytical results is usually negligibly small.
Do not use the symbols "^" or "**" for "raised to the power of" and use 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 |
Euler's constant and Pi are represented by "E" and PI" respectively.
