In various scientific and engineering fields, when we make measurements or do calculations, there is usually some uncertainty or margin of error involved. That's how this error propagation calculator can be used to evaluate how these uncertainties or errors in the mathematical calculations can affect the accuracy of the final result.
Calculating error propagation becomes effortless when using the error propagation calculator provided by Calculatored.
Error propagation, also known as propagation of uncertainty, is the process where uncertainties in measured values affect the precision of calculated results during mathematical operations.
When mathematical operations such as addition, subtraction, multiplication, or division are performed using measured values with associated uncertainties, the uncertainties can propagate to the final result.
When dealing with uncertainties in measured quantities, our error propagation calculator uses the following formulas to estimate errors in different mathematical operations.
\(ΔZ = \sqrt{(ΔX)^2 + (ΔY)^2}\)
\(ΔZ = Z \cdot \sqrt{(\dfrac{ΔX}{X})^2 + (\dfrac{ΔY}{Y})^2}\)
Addition (Z = X + Y):
\(ΔZ = \sqrt{(ΔX)^2 + (ΔY)^2}\)
Subtraction (Z = X - Y):
\(ΔZ = \sqrt{(ΔX)^2 + (ΔY)^2}\)
Multiplication (Z = X * Y):
\(ΔZ = Z \cdot \sqrt{(\dfrac{ΔX}{X})^2 + (\dfrac{ΔY}{Y})^2}\)
Division (Z = X/Y):
\(ΔZ = Z \cdot \sqrt{(\dfrac{ΔX}{X})^2 + (\dfrac{ΔY}{Y})^2}\)
Suppose you have two measurements:
Given values:
Now, calculate the error propagation under different situations by using their corresponding formulas:
Addition:
Subtraction:
Multiplication:
Division:
Result: Z = 2 ± 0.9
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