Rounding Calculator (Round, Round Up and Round Down)

Enter the number to round and the place to round to. You get the rounded, rounded-up and rounded-down results, plus other rounding methods, all at once.

Number to round

Round to (decimal places)

Give the place as a whole number: 0 = nearest whole number, 2 = nearest hundredth, -2 = nearest hundred. Positive numbers count places after the decimal point, negative numbers count places to the left.

Result

Enter a number and the place to round to in the fields on the left and press "Calculate". The result will appear here.

[ CLOSE ]

What you can do on this page
What is this calculation used for?
How to Use
Formula
Symbols and terms
- Symbols
- Terms
Good to know before you start
How to calculate it in Excel
How to calculate it in Google Sheets
How to calculate it in Python
How to write it in LaTeX and other math languages (copy and paste)
How to have ChatGPT do the calculation
DataChef Features
Related Features
NumberChef Calculators List

What you can do on this page

Enter a number and the place to round to, and you get the rounded, rounded-up and rounded-down results all at once
Round to any place you like: the nearest whole number, tenth, hundredth, ten, hundred and so on
The results of rounding methods used in computing and statistics, such as round half to even (banker's rounding), the floor function and the ceiling function, are listed too
A plain-language explanation of the formulas and copy-and-paste formulas for Excel, Google Sheets and Python are all on this page

On this page, "round" means the method taught in school: a digit of 5 or more rounds up, and an exact half goes away from zero (2.5 → 3, −2.5 → −3). This is the same as the Excel ROUND function, but it can differ from Python's round(), which rounds half to even.

What is this calculation used for?

Sales tax to the nearest cent (why your receipt can differ by a penny)

An item costs $3.98 and the sales tax rate is 7.25%. The tax is $3.98 \times 0.0725 = 0.28855$ dollars, which has to become a whole number of cents. Most states have sellers round to the nearest cent, with half a cent or more rounded up, so the tax is $0.29.
Tax on a whole order and tax item by item can come out a cent apart because of rounding. Knowing this, you can check receipts and invoices with confidence.

Rounding work hours (the 7-minute rule)

US federal rules allow employers to round clock-in and clock-out times to the nearest 5, 6 or 15 minutes, as long as it evens out over time. With 15-minute rounding, 1 to 7 minutes past the quarter hour round down and 8 to 14 minutes round up. So clocking in at 8:07 counts as 8:00, and 8:08 counts as 8:15.
Your paycheck is built from roundings like this, so knowing how they work lets you check your own hours and pay.

Why survey percentages do not add up to 100%

If three choices each get about one third of the votes, rounding each to the nearest tenth of a percent gives $33.3\% + 33.3\% + 33.3\% = 99.9\%$, not 100%.
This is not a counting mistake. It is simply what rounding does, and news charts often carry a note such as "Totals may not add up to 100% due to rounding". Knowing this helps you read statistics and charts correctly.

Ordering materials means rounding up (building and DIY)

Each box of floor tile covers 10 square feet, and the room is 124 square feet. You need $124 \div 10 = 12.4$ boxes, so you buy 13 (12 boxes would not be enough).
The number of tables for guests, buses for a field trip, boxes of medicine: whenever running short is a problem, rounding up is the right answer, not ordinary rounding. Choosing the right rounding method is part of the job.

Banker's rounding avoids bias in large data (statistics, finance, computing)

Always rounding an exact half up pushes totals and averages slightly upward when there is a lot of data. For example, the ten numbers 0.5, 1.5, …, 9.5 have an average of exactly 5.0. If you round each one first and then average, you get 5.5. With round half to even, half the ties go up and half go down, the bias cancels out, and the average stays at 5.0.
That is why round half to even is the standard in finance, where interest is calculated again and again, and inside the decimal arithmetic of many programming languages (the IEEE 754 standard).

Formula

Rounding to the nearest whole number

Standard notation (the usual math form)

$R$ $=$ $\lfloor$ $x$ $+$ $0.5$ $\rfloor$

In words (symbols replaced with words)

④ $R$: rounded result $=$ ③ $\lfloor$ ① $x$: number to round $+$ ② $0.5$: one half $\rfloor$

The formula in words

① Take the $x$: number to round

② add $0.5$: one half

③ drop everything after the decimal point with the floor function $\lfloor\ \rfloor$

④ and you get the $R$: rounded result

Quick example

Rounding 2.7 to the nearest whole number gives

$R$: rounded result $=$ $\lfloor$ number to round (2.7) $+$ one half (0.5) $\rfloor$

$2.7 + 0.5 = 3.2$

$\lfloor 3.2 \rfloor = 3$

Key idea

The school rule "if the next digit is 0 to 4, round down; if it is 5 to 9, round up" fits into one formula: add 0.5, then drop everything after the decimal point. An exact half such as 2.5 becomes 3.0 when you add 0.5, so it always rounds up to 3. For negative numbers, the usual method (and the one Excel ROUND uses) is to take off the minus sign, round, and put the sign back (−2.5 → round 2.5 to 3 → −3). The calculator on this page works this way too. Other methods, such as banker's rounding, which sends an exact half to the even side, are shown lower in the calculator results.

Rounding up (ceiling function)

Standard notation (the usual math form)

$R$ $=$ $\lceil$ $x$ $\rceil$

In words (symbols replaced with words)

③ $R$: rounded-up result $=$ ② $\lceil$ ① $x$: number to round $\rceil$

The formula in words

① Take the $x$: number to round

② move it up to the next whole number with the ceiling function $\lceil\ \rceil$ if there is any fraction left at all

③ and you get the $R$: rounded-up result

Quick example

Rounding 5.01 up to a whole number (even a leftover of 0.01 moves it up) gives

$R$: rounded-up result $=$ $\lceil$ number to round (5.01) $\rceil$

$\lceil 5.01 \rceil = 6$

Key idea

Rounding up always moves to the next value up unless the leftover is exactly 0. Use it when running short would be a problem, as in "Each box of tile covers 10 square feet. How many boxes do I need for 124 square feet?" (12.4 → 13 boxes). Watch out: there are two conventions for negative numbers. In everyday use and in the Excel ROUNDUP function, rounding up goes away from zero (−5.01 → −6). The ceiling function $\lceil\ \rceil$ in math goes toward +∞ (−5.01 → −5). The calculator on this page shows both results.

Rounding down (floor function)

Standard notation (the usual math form)

$R$ $=$ $\lfloor$ $x$ $\rfloor$

In words (symbols replaced with words)

③ $R$: rounded-down result $=$ ② $\lfloor$ ① $x$: number to round $\rfloor$

The formula in words

① Take the $x$: number to round

② remove everything after the decimal point with the floor function $\lfloor\ \rfloor$

③ and you get the $R$: rounded-down result

Quick example

Rounding 5.99 down to a whole number (however large the leftover, it stays at the lower number) gives

$R$: rounded-down result $=$ $\lfloor$ number to round (5.99) $\rfloor$

$\lfloor 5.99 \rfloor = 5$

Key idea

Rounding down (also called truncating) simply drops the leftover part. It is common with money and counts, for example when you ask how many full $5 tickets you can buy with $23 (4.6 → 4 tickets). Negative numbers have two conventions here too. In everyday use and in the Excel ROUNDDOWN function, rounding down goes toward zero (−5.01 → −5). The floor function $\lfloor\ \rfloor$ in math goes toward −∞ (−5.01 → −6). The calculator on this page shows both results.

Rounding to any place (rounding unit $q$)

Standard notation (the usual math form)

$R$ $=$ $\lfloor$ $x$ $\div$ $q$ $+$ $0.5$ $\rfloor$ $\times$ $q$

In words (symbols replaced with words)

⑥ $R$: rounded result $=$ ④ $\lfloor$ ① $x$: number to round $\div$ ② $q$: rounding unit $+$ ③ $0.5$: one half $\rfloor$ $\times$ ⑤ $q$: rounding unit

The formula in words

① Take the $x$: number to round

② divide it by the $q$: rounding unit to see how many $q$s it is

③ add $0.5$: one half

④ drop everything after the decimal point with the floor function $\lfloor\ \rfloor$ to get a whole number

⑤ multiply by the $q$: rounding unit again

⑥ and you get the $R$: rounded result

Quick example

Rounding 1234.5678 to the nearest hundred (rounding unit $q = 100$) gives

$R$: rounded result $=$ $\lfloor$ number to round (1234.5678) $\div$ rounding unit (100) $+$ one half (0.5) $\rfloor$ $\times$ rounding unit (100)

$1234.5678 \div 100 = 12.345678$

$12.345678 + 0.5 = 12.845678$

$\lfloor 12.845678 \rfloor \times 100 = 12 \times 100 = 1200$

Key idea

Choose the rounding unit $q$ like this: to the nearest hundredth → $q = 0.01$, to the nearest whole number → $q = 1$, to the nearest hundred → $q = 100$. (If $n$ is the place you round to, then $q = 10^{-n}$. The "Round to (decimal places)" box in this calculator is this $n$.) Rounding up and rounding down work the same way: $\lceil x \div q \rceil \times q$ and $\lfloor x \div q \rfloor \times q$ round to any place you like. "Count how many $q$s there are → round that count to a whole number → multiply by $q$ again" is the idea behind every kind of rounding.

The basic idea of rounding is: count how many rounding units q there are, round that count to a whole number, then multiply by q again. For ordinary rounding, the trick is "add 0.5, then round down". Different ways of handling an exact half give rise to the many rounding methods, such as banker's rounding.

Symbols and terms

Symbols

$x$	x	The number to round. (Example - a test average of 81.35)
$n$	n	The place to round to. 0 = the ones place, a positive number = $n$ places after the decimal point, a negative number = the tens, hundreds, thousands… place. (Example - to round to the nearest hundred, $n = -2$)
$q$	q	The rounding unit. A rounded result is always a multiple of $q$. $q = 10^{-n}$, so it is $0.01$ for the nearest hundredth and $100$ for the nearest hundred.
$R$	R	The rounded result. Its value depends on the rounding method (rounding, rounding up, rounding down and so on).
$\lfloor x \rfloor$	floor of x	The greatest integer less than or equal to $x$. For positive numbers it is the same as dropping the digits after the decimal point. (Example - $\lfloor 5.99 \rfloor = 5$. But for negative numbers, $\lfloor -5.01 \rfloor = -6$)
$\lceil x \rceil$	ceiling of x	The least integer greater than or equal to $x$. For positive numbers it is the same as rounding up. (Example - $\lceil 5.01 \rceil = 6$. But for negative numbers, $\lceil -5.01 \rceil = -5$)

Terms

rounding	Replacing a number that has too many digits with a simpler number, following a fixed rule. Ordinary rounding, rounding up and rounding down are all kinds of rounding.
approximate number	A number that is close to the exact value, such as "about 1,900 people". Rounding is the most common way to make one, and US students first practice it in Grade 3.
round half away from zero	The school rounding method - if the next digit is 0 to 4, round down; if it is 5 to 9, round up. An exact half such as 2.5 always rounds up (for negative numbers, away from zero - −2.5 → −3). It is what Excel ROUND does.
round up	A rounding method that moves up to the next value if there is any leftover at all. 5.01 rounded up to a whole number is 6. It is used when running short would be a problem (such as how many boxes of material to buy).
round down	A rounding method that drops the leftover completely. 5.99 rounded down to a whole number is 5. It is also called truncating, and it is common with money and counts.
banker's rounding (round half to even)	A method that, only for an exact half, rounds to the side that gives an even result (2.5 → 2, 3.5 → 4). Unlike always rounding a half up, it does not push totals and averages in one direction, so it is standard in statistics, finance and inside computers. Python's round() works this way.
floor function	A math function written $\lfloor x \rfloor$ that gives the nearest integer at or below $x$ (toward −∞). For positive numbers it matches rounding down, but for negative numbers it goes the other way, which is how it differs from everyday rounding down.
ceiling function	A math function written $\lceil x \rceil$ that gives the nearest integer at or above $x$ (toward +∞). For positive numbers it matches rounding up, but for negative numbers it goes the other way, which is how it differs from everyday rounding up.

Good to know before you start

Here is what helps you use the calculation on this page with real understanding, not just by pressing the button.

Place value (Grades 1–2)	Knowing which digits are the ones, tens, hundreds and thousands places Being able to picture which digits stay when asked to round to the nearest hundred
How decimals work (Grades 4–5)	Knowing which digits are the tenths and hundredths places Knowing how the decimal places relate, for example that ten 0.1s make 1
Rounding and approximate numbers (Grades 3–5)	Knowing what an approximate number such as "about 1,900" is used for Knowing that to round, you look at the digit one place to the right of the place you round to, and round down for 0 to 4 and up for 5 to 9
Negative numbers and the number line (Grade 6)	Seeing on the number line that -5 is greater than -6 Understanding what "toward zero" and "away from zero" mean when rounding negative numbers up or down

How to calculate it in Excel

Copy the whole table below and paste it into cell A1 in Excel. It works as is.

Table to round to the nearest whole number

Number to round x	2.7
Rounded result	=ROUND(B1,0)

Table to round up

Number to round x	5.01
Rounded-up result	=ROUNDUP(B1,0)

Table to round down

Number to round x	5.99
Rounded-down result	=ROUNDDOWN(B1,0)

Table to round to any place

Number to round x	1234.5678
Place n (2 = hundredth, 0 = whole number, -2 = hundred)	-2
Rounded result	=ROUND(B1,B2)

After pasting, B1 (and B2 in the fourth table) are your inputs, and the last row is calculated automatically.
The second argument of ROUND, ROUNDUP and ROUNDDOWN, "num_digits", means the same as "Round to (decimal places)" on this page (0 = whole number, 2 = hundredth, -2 = hundred).
Excel ROUND works like the rounding on this page: an exact half goes away from zero. ROUNDUP and ROUNDDOWN move away from zero and toward zero for negative numbers (ROUNDUP(-5.01,0) is -6).
For example, the first table shows 3 in B2, and the fourth table shows 1200 in B3.

How to calculate it in Google Sheets

Copy the whole table below and paste it into cell A1 in Google Sheets. It works as is.

Table to round to the nearest whole number

Number to round x	2.7
Rounded result	=ROUND(B1,0)

Table to round up

Number to round x	5.01
Rounded-up result	=ROUNDUP(B1,0)

Table to round down

Number to round x	5.99
Rounded-down result	=ROUNDDOWN(B1,0)

Table to round to any place

Number to round x	1234.5678
Place n (2 = hundredth, 0 = whole number, -2 = hundred)	-2
Rounded result	=ROUND(B1,B2)

ROUND, ROUNDUP and ROUNDDOWN work in Google Sheets exactly as in Excel. Copy the whole table, paste it into cell A1, and replace B1 (the number to round) with your own number.

How to calculate it in Python

from decimal import Decimal, ROUND_HALF_UP, ROUND_UP, ROUND_DOWN

number = Decimal("1234.5678")  # number to round (always pass it as a string to avoid the 0.1 error problem)
digits = -2                    # place to round to (2 = hundredth, 0 = whole number, -2 = hundred)

unit = Decimal(1).scaleb(-digits)  # rounding unit (100 when digits is -2)

rounded = number.quantize(unit, rounding=ROUND_HALF_UP)       # round (half away from zero)
rounded_up = number.quantize(unit, rounding=ROUND_UP)         # round up (away from zero)
rounded_down = number.quantize(unit, rounding=ROUND_DOWN)     # round down (toward zero)

print(f"Round: {rounded:f}")
print(f"Round up: {rounded_up:f}")
print(f"Round down: {rounded_down:f}")

Runs with the standard library only. Python's built-in round() uses round half to even (banker's rounding), so round(2.5) gives 2, which differs from school rounding. To round the school way, the safe choice is ROUND_HALF_UP from the decimal module, as in this example (in Python's decimal module, ROUND_HALF_UP sends an exact half away from zero).

How to write it in LaTeX and other math languages (copy and paste)

Rounding to the nearest whole number

R = ⌊x + 0.5⌋

R = \lfloor x + 0.5 \rfloor

<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
  <mrow>
    <mi>R</mi>
    <mo>=</mo>
    <mo>&#x230A;</mo>
    <mi>x</mi>
    <mo>+</mo>
    <mn>0.5</mn>
    <mo>&#x230B;</mo>
  </mrow>
</math>

R = |__ x + 0.5 __|

Floor[x + 0.5]

R := floor(x + 0.5);

R = floor(x + 0.5);

R = ⌊x + 0.5⌋

Rounding up (ceiling function)

R = ⌈x⌉

R = \lceil x \rceil

<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
  <mrow>
    <mi>R</mi>
    <mo>=</mo>
    <mo>&#x2308;</mo>
    <mi>x</mi>
    <mo>&#x2309;</mo>
  </mrow>
</math>

R = |~ x ~|

Ceiling[x]

R := ceil(x);

R = ceil(x);

R = ⌈x⌉

Rounding down (floor function)

R = ⌊x⌋

R = \lfloor x \rfloor

<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
  <mrow>
    <mi>R</mi>
    <mo>=</mo>
    <mo>&#x230A;</mo>
    <mi>x</mi>
    <mo>&#x230B;</mo>
  </mrow>
</math>

R = |__ x __|

Floor[x]

R := floor(x);

R = floor(x);

R = ⌊x⌋

Rounding to any place (rounding unit $q$)

R = ⌊x ÷ q + 0.5⌋ × q

R = \left\lfloor \frac{x}{q} + 0.5 \right\rfloor \times q

<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
  <mrow>
    <mi>R</mi>
    <mo>=</mo>
    <mo>&#x230A;</mo>
    <mfrac><mi>x</mi><mi>q</mi></mfrac>
    <mo>+</mo>
    <mn>0.5</mn>
    <mo>&#x230B;</mo>
    <mo>&#xD7;</mo>
    <mi>q</mi>
  </mrow>
</math>

R = |__ x/q + 0.5 __| xx q

Floor[x/q + 0.5] q

R := floor(x/q + 0.5) * q;

R = floor(x/q + 0.5) * q;

R = ⌊x/q + 0.5⌋ × q

How to have ChatGPT do the calculation

You are a calculation assistant. Do the following calculation by actually running Python code, and base your answer only on the numbers from the execution result (do not answer by mental math or guessing). Do not use Python's built-in round(), which rounds half to even. Use the decimal module (ROUND_HALF_UP and so on) instead.

Round the number 1234.5678 to the nearest hundred in the following three ways:
1. Round (an exact half goes away from zero)
2. Round up (away from zero)
3. Round down (toward zero)

Show the code you used and the numbers from the execution result.

How to Use

1

Enter your numbers

Type the numbers you want to calculate with into the input fields
2

Calculate

Press the "Calculate" button
3

Check the result

The result appears on the spot. The same page also explains the idea behind the calculation and the formula

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\(x\)	x	The number to round. (Example - a test average of 81.35)
\(n\)	n	The place to round to. 0 = the ones place, a positive number = \(n\) places after the decimal point, a negative number = the tens, hundreds, thousands… place. (Example - to round to the nearest hundred, \(n = -2\))
\(q\)	q	The rounding unit. A rounded result is always a multiple of \(q\). \(q = 10^{-n}\), so it is \(0.01\) for the nearest hundredth and \(100\) for the nearest hundred.
\(R\)	R	The rounded result. Its value depends on the rounding method (rounding, rounding up, rounding down and so on).
\(\lfloor x \rfloor\)	floor of x	The greatest integer less than or equal to \(x\). For positive numbers it is the same as dropping the digits after the decimal point. (Example - \(\lfloor 5.99 \rfloor = 5\). But for negative numbers, \(\lfloor -5.01 \rfloor = -6\))
\(\lceil x \rceil\)	ceiling of x	The least integer greater than or equal to \(x\). For positive numbers it is the same as rounding up. (Example - \(\lceil 5.01 \rceil = 6\). But for negative numbers, \(\lceil -5.01 \rceil = -5\))

Rounding Calculator (Round, Round Up and Round Down)

Table of Contents

What you can do on this page

What is this calculation used for?

Formula

Symbols and terms

Symbols

Terms

Good to know before you start

How to calculate it in Excel

How to calculate it in Google Sheets

How to calculate it in Python

How to write it in LaTeX and other math languages (copy and paste)

How to have ChatGPT do the calculation

How to Use

DataChef Features

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