Given a Formula with an Absolute Error in of , the Absolute Error is . The
Relative Error is . If , then
(1) |
(2) |
(3) | |||
(4) | |||
(5) |
(6) |
(7) |
Now consider addition of quantities with errors.
For ,
and
, so
(8) |
For division of quantities with
,
and
, so
(9) |
(10) |
For exponentiation of quantities with
(11) |
(12) |
(13) |
(14) |
(15) |
For Logarithms of quantities with
,
, so
(16) |
(17) |
For multiplication with
,
and
, so
(18) |
(19) |
For Powers,
with ,
, so
(20) |
(21) |
See also Absolute Error, Percentage Error, Relative Error
References
Abramowitz, M. and Stegun, C. A. (Eds.).
Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing.
New York: Dover, p. 14, 1972.
Bevington, P. R. Data Reduction and Error Analysis for the Physical Sciences. New York:
McGraw-Hill, pp. 58-64, 1969.
© 1996-9 Eric W. Weisstein