Calculator finds out absolute or relative error basing it on measured (calculated) and reference (ideal) value.

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Symbolic algebra

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What do you want to calculate today?#

Choose a scenario that best fits your needs

I know measured value (x) and reference values (

x_0

) and want to calculate absolute error (

\Delta x

)I know measured value (x) and reference values (

x_0

) and want to calculate relative error (

\delta x_{rel.}

)

Calculations data - enter values, that you know here#

Absolute error ( $\Delta x$ )		=>
Relative error ( $\delta x_{rel.}$ )		=>
Measured value (x)		<=
Reference values ( $x_0$ )		<=

Result: absolute error ( $\Delta x$ )#

Summary

Used formula

Show source

\Delta x=\left|x-x_0\right|

Result

Show source

\frac{39816339744831}{25000000000000000}

Numerical result

Show source

0.00159265358979324

Result step by step

1	Show source $\left\|3.14-3.14159265358979324\right\|$	Convert decimal to fraction	Decimal number can be converted into fraction with denominator 10, 100, 1000 etc.
2	Show source $\left\|\frac{157}{50}-3.14159265358979324\right\|$	Convert decimal to fraction	Decimal number can be converted into fraction with denominator 10, 100, 1000 etc.
3	Show source $\left\|\frac{157}{50}-\frac{78539816339744831}{25000000000000000}\right\|$	Common denominator	Before add two fractions, we need convert them into common denominator. We can find the optimal common denominator using the lowest common multiply (LCM) from both denominators.
4	Show source $\left\|\frac{157 \cdot 500000000000000-78539816339744831}{25000000000000000}\right\|$	Simplify arithmetic	-
5	Show source $\left\|\frac{78500000000000000-78539816339744831}{25000000000000000}\right\|$	Simplify arithmetic	-
6	Show source $\left\|\frac{-39816339744831}{25000000000000000}\right\|$	Absolute value	$\|c\| = \left \{ \begin{aligned} &c && \text{, if}\ c \ge 0 \\ &-c && \text{, if}\ c \lt 0 \end{aligned} \right.$
7	Show source $\frac{\left\|-39816339744831\right\|}{\left\|25000000000000000\right\|}$	Absolute value	$\|c\| = \left \{ \begin{aligned} &c && \text{, if}\ c \ge 0 \\ &-c && \text{, if}\ c \lt 0 \end{aligned} \right.$
8	Show source $\frac{39816339744831}{\left\|25000000000000000\right\|}$	Absolute value	$\|c\| = \left \{ \begin{aligned} &c && \text{, if}\ c \ge 0 \\ &-c && \text{, if}\ c \lt 0 \end{aligned} \right.$
9	Show source $\frac{39816339744831}{25000000000000000}$	Result	Your expression reduced to the simplest form known to us.

Numerical result step by step

1	Show source $\frac{39816339744831}{25000000000000000}$	Divided fraction	-
2	Show source $0.00159265358979324$	Result	Your expression reduced to the simplest form known to us.

Some facts#

Absolute error is the absolute value of the difference between measured value (calculated, approximate etc.) and reference value (ideal, theoretical etc.):

$\Delta x = |x-x_0|$
where:
- $\Delta x$ - absolute error,
- $x$ - measured, calculated or approximate value of variable $x$ ,
- $x_0$ - the reference value against which we calculate the error.
Relative error determines the size of the error made presented as part of the reference value:

$\delta x_{wzgl.} = \left|\dfrac{x-x_0}{x_0}\right|$
where:
- $\delta x_{rel.}$ - error expressed as a part of the reference value,
- $x$ - measured, calculated or approximate value of variable $x$ ,
- $x_0$ - the reference value against which we calculate the error.
When we determine the error, we are generally not trying to find out whether the value obtained is too large or too small, but only how big the error is. This is the reason why error formula has the absolute value form.
In the case of values with units (e.g. length measured in meters), the absolute error has the same units as the measured one. For example, an absolute error of length value is also the length.
Relative error has no units, no metter what do we measure. Relative error is often presented as percent.