is an option for various numerical operations which specifies how many effective digits of precision should be sought in the final result.
PrecisionGoal
is an option for various numerical operations which specifies how many effective digits of precision should be sought in the final result.
Details
- PrecisionGoal is an option for such functions as NIntegrate and NDSolve .
- PrecisionGoal->Automatic normally yields a precision goal equal to half the setting for WorkingPrecision .
- PrecisionGoal->Infinity specifies that precision should not be used as the criterion for terminating the numerical procedure. AccuracyGoal is typically used in this case.
- Even though you may specify PrecisionGoal->n, the results you get may sometimes have much less than n‐digit precision.
- In most cases, you must set WorkingPrecision to be at least as large as PrecisionGoal .
- PrecisionGoal effectively specifies the relative error allowed in a numerical procedure.
- With PrecisionGoal->p and AccuracyGoal->a, the Wolfram Language attempts to make the numerical error in a result of size x be less than 10^(-a)+TemplateBox[{x}, Abs]10^(-p).
Examples
open all close allBasic Examples (2)
Approximate an integral to at least 10 digits of precision:
Use accuracy (absolute error) as the basis for error control in solving an ODE:
The error is small:
Without specifying the PrecisionGoal , the error is much larger:
Scope (2)
Find a minimum with convergence criteria and :
Try with convergence criteria and :
Use a higher working precision to allow convergence:
Solve a differential equation using high-precision arithmetic:
Use AccuracyGoal and PrecisionGoal at half the 32-digit working precision:
This corresponds to the automatic setting used by NDSolve :
Related Guides
History
Introduced in 1991 (2.0) | Updated in 2003 (5.0)
Text
Wolfram Research (1991), PrecisionGoal, Wolfram Language function, https://reference.wolfram.com/language/ref/PrecisionGoal.html (updated 2003).
CMS
Wolfram Language. 1991. "PrecisionGoal." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2003. https://reference.wolfram.com/language/ref/PrecisionGoal.html.
APA
Wolfram Language. (1991). PrecisionGoal. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/PrecisionGoal.html
BibTeX
@misc{reference.wolfram_2025_precisiongoal, author="Wolfram Research", title="{PrecisionGoal}", year="2003", howpublished="\url{https://reference.wolfram.com/language/ref/PrecisionGoal.html}", note=[Accessed: 04-January-2026]}
BibLaTeX
@online{reference.wolfram_2025_precisiongoal, organization={Wolfram Research}, title={PrecisionGoal}, year={2003}, url={https://reference.wolfram.com/language/ref/PrecisionGoal.html}, note=[Accessed: 04-January-2026]}