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

ⓘ Hint: This calculator supports symbolic math. You can enter numbers, but also symbols like a, b, pi or even whole math expressions such as (a+b)/2. If you still don't sure how to make your life easier using symbolic algebra check out our another page: Symbolic calculations

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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)#

Used formulaShow sourceΔx=abs(xx0)\Delta x=abs\left(x-x_0\right)
ResultShow source15926535897931000000000000000\frac{1592653589793}{1000000000000000}
Numerical resultShow source0.0015926535897930.001592653589793
Result step by step
1Show sourceabs(3.143.141592653589793)abs\left(3.14-3.141592653589793\right)Convert decimal to fraction
2Show sourceabs(157503.141592653589793)abs\left(\frac{157}{50}-3.141592653589793\right)Convert decimal to fraction
3Show sourceabs(15750+31415926535897931000000000000000)abs\left(\frac{157}{50}+\frac{-3141592653589793}{1000000000000000}\right)Common denominator
4Show sourceabs(1572000000000000031415926535897931000000000000000)abs\left(\frac{157 \cdot 20000000000000-3141592653589793}{1000000000000000}\right)Simplify arithmetic
5Show sourceabs(314000000000000031415926535897931000000000000000)abs\left(\frac{3140000000000000-3141592653589793}{1000000000000000}\right)Simplify arithmetic
6Show sourceabs(15926535897931000000000000000)abs\left(\frac{-1592653589793}{1000000000000000}\right)Absolute value
7Show sourceabs(1592653589793)abs(1000000000000000)\frac{abs\left(-1592653589793\right)}{abs\left(1000000000000000\right)}Absolute value
8Show source1592653589793abs(1000000000000000)\frac{1592653589793}{abs\left(1000000000000000\right)}Absolute value
9Show source15926535897931000000000000000\frac{1592653589793}{1000000000000000}Result
Numerical result step by step
1Show source0.0015926535897930.001592653589793Result

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|
    • 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|
    • 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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