# Error Calculation

by SS2006
Tags: calculation, error
 P: 84 as good as i am in physics, i just didnt try to understand error calculation can someone give me 2 easy ways to calculate error in addition for example 5 +- 0.2 + 6 +- 0.1 and in mulitplication, like my newest lab i have f = m tiems g and the mass is +- 0.2 and gravity is +- 0.1 for example mas is 25 g lets say, and gravity 9.8 so ya easiest way to calculate error in multi, and additio please :) thanks
 P: 84 ok, sot he final asnwer would be 11 +- 0.3 ? how bout mulitplication thats the harde rone i need this b4 tomorrow! lets say 4 +- 0.2 X 5 +- 0.3 thanks
HW Helper
P: 1,327

## Error Calculation

 Quote by SS2006 ok, sot he final asnwer would be 11 +- 0.3 ?
You're doing fine !!! Try the same method on multiplication question.
 P: 84 ok im quite confused bout the mulitplication one lets say 4 X 4 and 0.2 is the +/- error on both of them, can you just solve that one and show what u did
 P: 84 hmm is 4 +- 0.2 X 4 +- 0.2 16 +- 1.6? if it is im aliright, just lemme know
 Sci Advisor HW Helper P: 1,327 (i) minimum product [4-0.2]*[4-0.2]=14.44 (ii) maximum product [4+0.2]*[4+0.2]= 17.64 (iii) product without error 4*4 = 16 (a) (iii)-minimum 16-14.44 = 1.56 (b) max - (iii) = 17.64-16 = 1.64 Error in product is +/- what? well +/- 1.64 does include the value of your lower error (1.56), but actually overestimates it. If this is experimental data, it is valid to state there is +/- 1.64 (units) error in the result (or 16 +/- 1.64)
 HW Helper P: 1,449 Error analysis is quite an advance topic. Therefore one usually get the formulae to calculate the error in a value (say Z) as a result of the errors in the values it depends on (say A and B). In the following formulae the errors in the values are indicated by deltas. Firstly the error in a value obtained from a sum or difference calculation are given by: $$(\Delta Z)^2=(\Delta A)^2+(\Delta B)^2$$ The error in you first example will therefore be 0.2 In values obtained from multiplication and division calculations one sees the relative error - that is what fraction is the error of the value. The formula for calculating the error in a value obtained from multiplication/division is: $$\left(\frac{\Delta Z}{Z}\right)^2=\left(\frac{\Delta A}{A}\right)^2+\left(\frac{\Delta B}{B}\right)^2$$ If your mass is 25 kg then the resulting force is 245 +/- 3 N.