Relative and absolute error calculator
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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Calculations data - enter values, that you know here#

Absolute error (Δx\Delta x)
=>
Relative error (δxrel.\delta x_{rel.})
=>
Measured value (x)
<=
Reference values (x0x_0)
<=

Result: absolute error (Δx\Delta x)#

Summary
Used formulaShow sourceΔx=xx0\Delta x=\left|x-x_0\right|
ResultShow source3981633974483125000000000000000\frac{39816339744831}{25000000000000000}
Numerical resultShow source0.001592653589793240.00159265358979324
Result step by step
1Show source3.143.14159265358979324\left|3.14-3.14159265358979324\right|Convert decimal to fractionDecimal number can be converted into fraction with denominator 10, 100, 1000 etc.
2Show source157503.14159265358979324\left|\frac{157}{50}-3.14159265358979324\right|Convert decimal to fractionDecimal number can be converted into fraction with denominator 10, 100, 1000 etc.
3Show source157507853981633974483125000000000000000\left|\frac{157}{50}-\frac{78539816339744831}{25000000000000000}\right|Common denominatorBefore 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.
4Show source1575000000000000007853981633974483125000000000000000\left|\frac{157 \cdot 500000000000000-78539816339744831}{25000000000000000}\right|Simplify arithmetic-
5Show source785000000000000007853981633974483125000000000000000\left|\frac{78500000000000000-78539816339744831}{25000000000000000}\right|Simplify arithmetic-
6Show source3981633974483125000000000000000\left|\frac{-39816339744831}{25000000000000000}\right|Absolute valuec={c, if c0c, if c<0|c| = \left \{ \begin{aligned} &c && \text{, if}\ c \ge 0 \\ &-c && \text{, if}\ c \lt 0 \end{aligned} \right.
7Show source3981633974483125000000000000000\frac{\left|-39816339744831\right|}{\left|25000000000000000\right|}Absolute valuec={c, if c0c, if c<0|c| = \left \{ \begin{aligned} &c && \text{, if}\ c \ge 0 \\ &-c && \text{, if}\ c \lt 0 \end{aligned} \right.
8Show source3981633974483125000000000000000\frac{39816339744831}{\left|25000000000000000\right|}Absolute valuec={c, if c0c, if c<0|c| = \left \{ \begin{aligned} &c && \text{, if}\ c \ge 0 \\ &-c && \text{, if}\ c \lt 0 \end{aligned} \right.
9Show source3981633974483125000000000000000\frac{39816339744831}{25000000000000000}ResultYour expression reduced to the simplest form known to us.
Numerical result step by step
1Show source0.001592653589793240.00159265358979324The original expression-
2Show source0.001592653589793240.00159265358979324ResultYour 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.):
    Δx=xx0\Delta x = |x-x_0|
    where:
    • Δx\Delta x - absolute error,
    • xx - measured, calculated or approximate value of variable xx,
    • x0x_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:
    δxwzgl.=xx0x0\delta x_{wzgl.} = \left|\dfrac{x-x_0}{x_0}\right|
    where:
    • δxrel.\delta x_{rel.} - error expressed as a part of the reference value,
    • xx - measured, calculated or approximate value of variable xx,
    • x0x_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.

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