# Q & A: calculating error bars of a square

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Most recent answer: 02/08/2015
Q:
How to calculate error bars? I need the equation used to give error bars limits.eg:I am given with the value L = 6.0 ± 0.4I am supposed to find the value of L ² with uncertainties. (Including the ± value).I know how to do when logarithms are involved. What i don't now is how to do when a normal value is given.
- Power (age 20)
USA
A:

This is easy once you think about what the symbols mean. You say L=6.0±0.4. That means that you're pretty confident that L is in the range 5.6 to 6.4. So you're exactly equally confident that L2 is in the range 5.62 to 6.42. That's the range 31.36 to 40.96, which you could write as 36.16±4.8.

Usually you then choose to write that in some simpler, approximate form. (The original error bars were most likely some sort of guess anyway.) Say you call the range 31.4 to 41.0. You could call that 36.2±4.8. Or, if you want to keep your central estimate of L2 the same as the square of your central estimate of L, you might write 36±5. In more extreme cases you might use separate + and - error bars.

To relate to your familiar log error bars, notice that  the initial natural log (ln) error bars were about 0.4/6= 0.066. Squaring means doubling the log, so the new error bars on ln(L2) would be ±2*0.066=±0.132 That's a little less than one part in 7, so our error bars of 5 out of 36 agree.

Mike W.

(published on 02/08/2015)