Round
✖
Round
Details
- Mathematical function, suitable for both symbolic and numerical manipulation.
- Round rounds numbers of the form x .5 toward the nearest even integer.
- Round[x] returns an integer when x is any numeric quantity, whether or not it is an explicit number.
- Round[x] applies separately to real and imaginary parts of complex numbers.
- If a is not a real number, Round[x,a] is given by the formula Round[x,a]a Round[x/a]. »
- For exact numeric quantities, Round internally uses numerical approximations to establish its result. This process can be affected by the setting of the global variable $MaxExtraPrecision.
- Round automatically threads over lists. »
Examples
open allclose allBasic Examples (3)Summary of the most common use cases
https://wolfram.com/xid/0y8jwa-l5f
https://wolfram.com/xid/0y8jwa-p0b
Round to the nearest multiple of 10:
https://wolfram.com/xid/0y8jwa-ete
Plot the function over a subset of the reals:
https://wolfram.com/xid/0y8jwa-gq6hjz
Scope (32)Survey of the scope of standard use cases
Numerical Evaluation (8)
https://wolfram.com/xid/0y8jwa-l274ju
https://wolfram.com/xid/0y8jwa-nyer6m
https://wolfram.com/xid/0y8jwa-2lfl8j
https://wolfram.com/xid/0y8jwa-cksbl4
Value at two consecutive half-integers:
https://wolfram.com/xid/0y8jwa-02qupd
https://wolfram.com/xid/0y8jwa-hfml09
Single-argument Round always returns an exact result:
https://wolfram.com/xid/0y8jwa-shjc09
The two-argument form tracks the precision of the second argument:
https://wolfram.com/xid/0y8jwa-ba2tyl
Evaluate efficiently at high precision:
https://wolfram.com/xid/0y8jwa-ra768p
https://wolfram.com/xid/0y8jwa-28t5ra
Round can deal with real‐valued intervals:
https://wolfram.com/xid/0y8jwa-zrrkxk
Compute the elementwise values of an array using automatic threading:
https://wolfram.com/xid/0y8jwa-thgd2
Or compute the matrix Round function using MatrixFunction:
https://wolfram.com/xid/0y8jwa-o5jpo
Compute average-case statistical intervals using Around:
https://wolfram.com/xid/0y8jwa-cw18bq
Specific Values (6)
Values of Round at fixed points:
https://wolfram.com/xid/0y8jwa-nww7l
https://wolfram.com/xid/0y8jwa-b38rdw
Value at Infinity:
https://wolfram.com/xid/0y8jwa-bmqd0y
https://wolfram.com/xid/0y8jwa-ia2x93
Manipulate Round symbolically:
https://wolfram.com/xid/0y8jwa-emt
Find a value of x for which Round[x,2]=2:
https://wolfram.com/xid/0y8jwa-f2hrld
https://wolfram.com/xid/0y8jwa-cri30r
Visualization (4)
Plot the Round function:
https://wolfram.com/xid/0y8jwa-ecj8m7
Visualize the two-argument form:
https://wolfram.com/xid/0y8jwa-4ttbhz
Plot Round in three dimensions:
https://wolfram.com/xid/0y8jwa-i75zi3
Visualize Round in the complex plane:
https://wolfram.com/xid/0y8jwa-lasc33
Function Properties (10)
Round[x] is defined for all real and complex inputs:
https://wolfram.com/xid/0y8jwa-cl7ele
https://wolfram.com/xid/0y8jwa-c4ycek
Round[x,a] is defined for a!=0:
https://wolfram.com/xid/0y8jwa-i38lcr
Round can produce infinitely large and small results:
https://wolfram.com/xid/0y8jwa-evf2yr
Round is an odd function in its first argument:
https://wolfram.com/xid/0y8jwa-7ve37k
Round is an even function in its second argument:
https://wolfram.com/xid/0y8jwa-tpcjkj
Round is not an analytic function:
https://wolfram.com/xid/0y8jwa-h5x4l2
It has both singularities and discontinuities:
https://wolfram.com/xid/0y8jwa-mdtl3h
https://wolfram.com/xid/0y8jwa-mn5jws
Round is nondecreasing:
https://wolfram.com/xid/0y8jwa-nlz7s
https://wolfram.com/xid/0y8jwa-86b1jl
Round is not injective:
https://wolfram.com/xid/0y8jwa-poz8g
https://wolfram.com/xid/0y8jwa-ctca0g
Round is not surjective:
https://wolfram.com/xid/0y8jwa-cxk3a6
https://wolfram.com/xid/0y8jwa-frlnsr
Round is neither non-negative nor non-positive:
https://wolfram.com/xid/0y8jwa-84dui
Round is neither convex nor concave:
https://wolfram.com/xid/0y8jwa-8kku21
Differentiation and Integration (4)
First derivative with respect to x:
https://wolfram.com/xid/0y8jwa-krpoah
First derivative with respect to a:
https://wolfram.com/xid/0y8jwa-b65mp5
https://wolfram.com/xid/0y8jwa-vqq
https://wolfram.com/xid/0y8jwa-ww5hxj
Applications (2)Sample problems that can be solved with this function
https://wolfram.com/xid/0y8jwa-fqgjbm
https://wolfram.com/xid/0y8jwa-b0ckjn
Click the bars to hear the name of the country and its rounded GDP per capita:
https://wolfram.com/xid/0y8jwa-g97wzu
https://wolfram.com/xid/0y8jwa-hmm98
Properties & Relations (6)Properties of the function, and connections to other functions
Negative numbers also round to the nearest integer:
https://wolfram.com/xid/0y8jwa-d0m
Round[x,a] gives the multiple of a nearest to x:
https://wolfram.com/xid/0y8jwa-fu8wbe
In general, it can be expressed in terms of the one-argument form as follows:
https://wolfram.com/xid/0y8jwa-hxrbxh
https://wolfram.com/xid/0y8jwa-5gz5ne
Round[x,-a] is equal to Round[x,a]:
https://wolfram.com/xid/0y8jwa-nkqbcu
At midpoints, Round rounds toward even integers:
https://wolfram.com/xid/0y8jwa-ddh
https://wolfram.com/xid/0y8jwa-nsf
This is also true of the two-argument form, where it rounds toward even multiples:
https://wolfram.com/xid/0y8jwa-psmxr8
https://wolfram.com/xid/0y8jwa-6r
https://wolfram.com/xid/0y8jwa-yqm
Possible Issues (1)Common pitfalls and unexpected behavior
Round does not automatically resolve the value:
https://wolfram.com/xid/0y8jwa-cc4
https://wolfram.com/xid/0y8jwa-tfk
Wolfram Research (1988), Round, Wolfram Language function, https://reference.wolfram.com/language/ref/Round.html (updated 2007).
Text
Wolfram Research (1988), Round, Wolfram Language function, https://reference.wolfram.com/language/ref/Round.html (updated 2007).
Wolfram Research (1988), Round, Wolfram Language function, https://reference.wolfram.com/language/ref/Round.html (updated 2007).
CMS
Wolfram Language. 1988. "Round." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2007. https://reference.wolfram.com/language/ref/Round.html.
Wolfram Language. 1988. "Round." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2007. https://reference.wolfram.com/language/ref/Round.html.
APA
Wolfram Language. (1988). Round. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Round.html
Wolfram Language. (1988). Round. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Round.html
BibTeX
@misc{reference.wolfram_2024_round, author="Wolfram Research", title="{Round}", year="2007", howpublished="\url{https://reference.wolfram.com/language/ref/Round.html}", note=[Accessed: 21-January-2025
]}
BibLaTeX
@online{reference.wolfram_2024_round, organization={Wolfram Research}, title={Round}, year={2007}, url={https://reference.wolfram.com/language/ref/Round.html}, note=[Accessed: 21-January-2025
]}