# Propagation of Errors

**Propagation of Errors.**

(1) **Error in sum of the quantities :** Suppose *z* = *x* + *y*

Let

Δ*x* = absolute error in measurement of *x*

Δ*y* = absolute error in measurement of *y*

Δ*z* = absolute error in calculation of *z*

The maximum absolute error in *z* is

Percentage error in the value of

(2) **Error in difference of the quantities : **Suppose *z* = *x* – *y*

Let

Δ*x* = absolute error in measurement of *x*,

Δ*y* = absolute error in measurement of *y*

Δ*z* = absolute error in calculation of *z*.

The maximum absolute error in *z* is

Percentage error in the value of

(3) **Error in product of quantities :** Suppose *z* = *x* ´ *y*

Let

Δ*x* = absolute error in measurement of *x*,

Δ*y* = absolute error in measurement of *y*

Δ*z* = absolute error in calculation of *z*.

The maximum fractional error in *z* is

Percentage error in the value of *z* = (Percentage error in value of *x*) + (Percentage error in value of *y*)

(4) **Error in division of quantities :** Suppose z=x / y

Let

Δ*z* = absolute error in measurement of *z*,

Δ*x* = absolute error in measurement of *x*

Δ*y* = absolute error in calculation of *y*.

The maximum fractional error in *z* is

Percentage error in the value of *z *= (Percentage error in value of *x*) + (Percentage error in value of *y*)

(5) **Error in quantity raised to some power :** Suppose

Let

Δ*x* = absolute error in measurement of *x*,

Δ*y* = absolute error in measurement of *y*

Δ*z* = absolute error in calculation of *z*

The maximum fractional error in *z* is

Percentage error in the value of *z* = *n *(Percentage error in value of *x*) + *m* (Percentage error in value of *y*)