round

Round to nearest decimal or integer

Syntax

Y = round(X)

Y = round(X,N)

Y = round(X,N,type)

Y = round(___,TieBreaker=direction)

Y = round(t)

Y = round(t,unit)

Description

Y = round(X) rounds each element of X to the nearest integer. In the case of a tie, where an element has a fractional part of 0.5 (within roundoff error) in decimal, the round function rounds away from zero to the nearest integer with larger magnitude.

Y = round(X,N) rounds to N digits:

• N > 0: round to N digits to the right of the decimal point.

• N = 0: round to the nearest integer.

• N < 0: round to N digits to the left of the decimal point.

Y = round(X,N,type) specifies the type of rounding. Specify "significant" to round to N significant digits (counted from the leftmost digit). In this case, N must be a positive integer.

Y = round(___,TieBreaker=direction) rounds ties as specified by direction. Use this argument after any of the input argument combinations in the previous syntaxes.

Y = round(t) rounds each element of the duration array t to the nearest number of seconds.

Y = round(t,unit) rounds each element of t to the nearest number of the specified unit of time.

Examples

Round Matrix Elements

Round the elements of a 2-by-2 matrix to the nearest integer.

X = [2.11 3.5; -3.5 0.78];
Y = round(X)

Y = 2×2

     2     4
    -4     1

Round to Specified Number of Decimal Digits

Round pi to the nearest 3 decimal digits.

Y = round(pi,3)

Y = 
3.1420

Round to Nearest Multiple of 100

Round the number 863178137 to the nearest multiple of 100.

round(863178137,-2)

ans = 
863178100

Round Elements to Specified Number of Significant Digits

Round the elements of a vector to retain 2 significant digits.

X = [1253 1.345 120.44]

X = 1×3
103 ×

    1.2530    0.0013    0.1204

Y = round(X,2,"significant")

Y = 1×3
103 ×

    1.3000    0.0013    0.1200

Control Number Display While Rounding

The format command controls how MATLAB® displays numbers at the command line. If a number has extra digits that cannot be displayed in the current format, then MATLAB automatically rounds the number for display purposes. This display can lead to unexpected results when combined with the round function.

Consider the result of this subtraction operation, which displays 5 digits.

format short
x = 112.05 - 110

x = 
2.0500

The displayed result is 2.0500, which looks like a tie. However, due to the floating-point arithmetic error, the tie at a fractional part of 0.5 is not within roundoff error.

Based on the displayed value of x, rounding x to 1 decimal should return 2.1.

y = round(x,1)

y = 
2

In fact, the problem here is that MATLAB is rounding x to 5 digits for display purposes. The round function returns the correct answer. Confirm the answer by viewing x with format long, which displays x rounded to 15 digits.

format long
x

x = 
   2.049999999999997

For comparison, show the rounding results for a tie that is within roundoff error and for a tie that is not within roundoff error.

x1 = 2.05

x1 = 
   2.050000000000000

y1 = round(x1,1)

y1 = 
   2.100000000000000

x2 = 2.05 - eps(2.05)

x2 = 
   2.049999999999999

y2 = round(x2,1)

y2 = 
     2

Specify Rounding Direction for Ties

Create a vector of decimals that have ties, that is, decimals with a fractional part of 0.5 (within roundoff error).

X = -2.5:1:2.5

X = 1×6

   -2.5000   -1.5000   -0.5000    0.5000    1.5000    2.5000

Round the ties to the nearest even and odd integers.

Yeven = round(X,TieBreaker="even")

Yeven = 1×6

    -2    -2     0     0     2     2

Yodd = round(X,TieBreaker="odd")

Yodd = 1×6

    -3    -1    -1     1     1     3

Round the ties towards positive and negative infinity.

Yplusinf = round(X,TieBreaker="plusinf")

Yplusinf = 1×6

    -2    -1     0     1     2     3

Yminusinf = round(X,TieBreaker="minusinf")

Yminusinf = 1×6

    -3    -2    -1     0     1     2

Round the ties away from zero and towards zero.

Yfromzero = round(X,TieBreaker="fromzero")

Yfromzero = 1×6

    -3    -2    -1     1     2     3

Ytozero = round(X,TieBreaker="tozero")

Ytozero = 1×6

    -2    -1     0     0     1     2

Round Duration Values

Round each value in a duration array to the nearest number of seconds.

t = hours(8) + minutes(29:31) + seconds(1.3:0.5:2.3);
t.Format = "hh:mm:ss.SS"

t = 1×3 duration
   08:29:01.30   08:30:01.80   08:31:02.30

Y1 = round(t)

Y1 = 1×3 duration
   08:29:01.00   08:30:02.00   08:31:02.00

Round each value in t to the nearest number of hours.

Y2 = round(t,"hours")

Y2 = 1×3 duration
   08:00:00.00   09:00:00.00   09:00:00.00

Input Arguments

X — Input array

scalar | vector | matrix | multidimensional array | table | timetable

Input array, specified as a scalar, vector, matrix, multidimensional array, table, or timetable. For complex X, round treats the real and imaginary parts independently.

X must be single, double, table, or timetable when you use round with more than one input.

round converts logical and char elements of X into double values.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 | char | logical | table | timetable
Complex Number Support: Yes

N — Number of digits

scalar integer

Number of digits, specified as a scalar integer. When you specify N, the round(X,N) function rounds X to the nearest multiple of 10^—N.

If you specify the "significant" rounding type, then N must be a positive integer.

type — Rounding type

"decimals" (default) | "significant"

Rounding type, specified as "decimals" or "significant". The rounding type determines whether round considers digits in relation to the decimal point or the overall number of significant digits. N must be a positive integer when you specify "significant". In that case, the round function rounds to the nearest number with N significant digits.

The default value is "decimals", so that round(X,N,"decimals") is equivalent to round(X,N).

Example: round(3132,2,"significant") returns 3100, which is the closest number to 3132 that has 2 significant digits.

Data Types: char | string

direction — Direction to break ties

"fromzero" (default) | "tozero" | "even" | "odd" | "plusinf" | "minusinf"

Direction to break ties, specified as one of these values:

• "fromzero" — Round ties away from zero to the nearest integer with larger magnitude.

• "tozero" — Round ties towards zero to the nearest integer with smaller magnitude.

• "even" — Round ties to the nearest even integer.

• "odd" — Round ties to the nearest odd integer.

• "plusinf" — Round ties towards positive infinity to the nearest integer with larger value.

• "minusinf" — Round ties towards negative infinity to the nearest integer with smaller value.

Ties are rare. When using round(X,N,TieBreaker=direction), a tie occurs only when X * 10^N is within roundoff error of a point halfway between two consecutive integers, that is, X * 10^N has a fractional part of 0.5 (within roundoff error) in decimal.

Example: round(2.015,2,TieBreaker="even")

t — Input duration

duration array

Input duration, specified as a duration array.

unit — Unit of time

"seconds" (default) | "minutes" | "hours" | "days" | "years"

Unit of time, specified as "seconds", "minutes", "hours", "days", or "years". A duration of 1 year is equal to exactly 365.2425 24-hour days.

Data Types: char | string

Tips

• format short and format long both display rounded numbers. This display can cause unexpected results when combined with the round function.

• For display purposes, use sprintf to control the exact display of a number as a string. For example, to display exactly 2 decimal digits of pi (and no trailing zeros), use sprintf("%.2f",pi).

Extended Capabilities

Tall Arrays

Calculate with arrays that have more rows than fit in memory.

The round function fully supports tall arrays. For more information, see Tall Arrays.

C/C++ Code Generation

Generate C and C++ code using MATLAB® Coder™.

Usage notes and limitations:

• Code generation supports only the syntax Y = round(X).

GPU Code Generation

Generate CUDA® code for NVIDIA® GPUs using GPU Coder™.

Usage notes and limitations:

• Code generation supports only the syntax Y = round(X).

Thread-Based Environment

Run code in the background using MATLAB® backgroundPool or accelerate code with Parallel Computing Toolbox™ ThreadPool.

This function fully supports thread-based environments. For more information, see Run MATLAB Functions in Thread-Based Environment.

GPU Arrays

Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.

The round function supports GPU array input with these usage notes and limitations:

• These syntaxes are not supported:

  Y = round(X,N)

  Y = round(X,N,type)

  Y = round(___,TieBreaker=direction)

For more information, see Run MATLAB Functions on a GPU (Parallel Computing Toolbox).

Distributed Arrays

Partition large arrays across the combined memory of your cluster using Parallel Computing Toolbox™.

This function fully supports distributed arrays. For more information, see Run MATLAB Functions with Distributed Arrays (Parallel Computing Toolbox).

Version History

Introduced before R2006a

R2023a: Perform calculations directly on tables and timetables

The round function can calculate on all variables within a table or timetable without indexing to access those variables. All variables must have data types that support the calculation. For more information, see Direct Calculations on Tables and Timetables.

R2022a: Control tiebreak behavior

Specify how to break ties by using the TieBreaker name-value argument. For example, round(X,TieBreaker="tozero") rounds ties towards zero.

R2022a: round returns consistent results for ties

Starting in R2022a, the round function always rounds ties away from zero to the nearest multiple of 10^—N with larger magnitude by default. For example:

X = 1.015:5.015;
N = 2;
Y = round(1.015:5.015,2)

Y =
    1.0200    2.0200    3.0200    4.0200    5.0200

In previous releases, the round function sometimes returned inconsistent results for ties by default. In the previous example, for instance, the second and third elements were rounded towards zero to 2.01 and 3.01, respectively.

R2014b: Rounding to specified number of digits

In R2014b, these syntaxes were added to round to any number of decimal or significant digits and to round duration values:

Y = round(X,N)
Y = round(X,N,type)
Y = round(t)  
Y = round(t,unit)   

Older versions of MATLAB^® support only this syntax, which rounds to the nearest integer:

Y = round(X)