Arithmetic
Rounding Calculator
Round any number to a set number of decimal places or to the nearest place value — and switch between round half up, banker's rounding, ceiling, floor, and more. The deciding digit and every step are shown live as you type.
Round a number
Round to
Rounding method
Exact halves go to the larger value. The everyday rule taught in school.
Rounded to 2 decimal places
3.14
3.14159 rounds down to 3.14
3.143.14163.15
Try an example
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The basics
What does it mean to round a number?
Rounding replaces a number with a nearby, simpler value to a chosen level of precision. Every rounding decision comes down to two things: the place you keep, and the single deciding digit just to its right. Read that digit, apply one rule, and drop the rest.
keep up to the rounding place
The rounding place
The place you round to is the last digit you keep — a decimal place like the hundredths, or a column like the nearest ten or hundred. Everything past it is dropped.
3.14|159 → keep 3.14
check the next digit only
The deciding digit
Only the first digit to the right of the rounding place matters. If it is large the kept digit goes up; if it is small the kept digit stays. The digits further along never change the decision.
deciding digit 5 → round up
Method
How to round, step by step
Four steps round any number to any place — the calculator above runs exactly these.
- 1
Find the rounding place
Identify the digit you want to keep — the tenths, the hundredths, the nearest hundred, whatever the task asks for.
round 3.14159 to the hundredths - 2
Read the deciding digit
Look at the first digit to the right of that place. This single digit — and nothing after it — decides the result.
deciding digit = 1 - 3
Apply the rule
Round half up: if the deciding digit is 5 or more, add one to the kept digit; if it is 4 or less, leave it. Other methods change only how exact halves are handled.
1 < 5 → round down - 4
Write the result
Drop every digit past the rounding place and write what remains. That is your rounded number.
3.14159 ≈ 3.14
Worked examples
See it across cases
The same procedure handles decimals, big place values, the exact-half tie, and negatives. Each tab computes the working from the rule.
Round 3.14159 to the 2 decimal places
Deciding digit: 1
Test: 1 < 5 → round down
3.14159 ≈ 3.14
Compare methods
One number, every method
Methods only ever disagree on the exact-half tie. Type a number and watch all six rounding rules resolve it at once — the fastest way to settle “is 2.5 a 2 or a 3?”
Round to
decimal places
Rounding 2.5 to the whole number, each method gives:
Round half up
Half up
3
Round half down
Half down
2
Round half to even
Banker's
2
Round up (ceiling)
Ceiling
3
Round down (floor)
Floor
2
Truncate (chop)
Truncate
2
Notice how the methods only disagree on the exact-half tie — every other digit rounds the same way.
Reference
The six rounding methods
Most rounding you meet is round half up. The others exist to handle ties differently or to force a direction — here is when each one is used.
Round half up
Half up
Exact halves go to the larger value. The everyday rule taught in school.
Round half down
Half down
Exact halves go to the smaller value. The mirror of round half up.
Round half to even
Banker's
Exact halves go to the nearest even digit. Removes upward bias in statistics and finance.
Round up (ceiling)
Ceiling
Always rounds toward positive infinity, halves or not.
Round down (floor)
Floor
Always rounds toward negative infinity, halves or not.
Truncate (chop)
Truncate
Drops the extra digits with no rounding — always toward zero.
Place values
Where each place sits
Rounding “to the nearest X” just points at a column. Left of the decimal the places grow by tens; right of it they shrink by tenths.
Nearest thousand
Thousand
103 = 1000
Nearest hundred
Hundred
102 = 100
Nearest ten
Ten
101 = 10
Nearest whole number
Whole
100 = 1
Nearest tenth
Tenth
10-1 = 0.1
Nearest hundredth
Hundredth
10-2 = 0.01
Nearest thousandth
Thousandth
10-3 = 0.001
Quick chart
Round one number to every place
Enter any value and see it rounded to every place at a glance — the answer to “round X to the nearest tenth / hundred / thousand” without re-running the tool seven times.
to every place (round half up)
Nearest thousand
1000
Nearest hundred
1200
Nearest ten
1230
Nearest whole number
1235
Nearest tenth
1234.6
Nearest hundredth
1234.57
Nearest thousandth
1234.568
Where it shows up
Why rounding matters
A quiet operation that shapes money, measurements, and data every day.
round to the cent
Money
Prices, taxes, and interest are rounded to two decimal places. Banks lean on banker's rounding so the cents don't drift upward over millions of transactions.
significant figures
Science & measurement
A result can only be as precise as its instrument, so measurements are rounded to a sensible number of significant figures rather than carrying false precision.
clean summaries
Data & reports
Dashboards round long decimals to readable figures. Choosing the method keeps totals from mysteriously failing to add up.
Worth knowing
Rules and pitfalls
A handful of habits keep rounding accurate — and a few traps catch almost everyone.
round once, at the end
Don't round twice
Rounding an already-rounded number compounds the error. Keep full precision through the calculation and round only the final answer.
the next digit only
Ignore the trailing digits
Only the deciding digit matters. 1.49 still rounds down to 1, because the deciding digit is 4 — the 9 after it is irrelevant.
ties split the methods
Halves are the only fork
Every method agrees except on an exact half. If your number has no tie, the method you pick makes no difference at all.
sign stays with the value
Negatives flip direction
For ceiling and floor, “up” and “down” mean toward positive or negative infinity — so the floor of a negative number is more negative, not closer to zero.
binary can't store 0.1
Float surprises
Computers store decimals in binary, so a stored value like 2.675 is really a hair under 2.675 and can round “wrong.” This tool nudges past that so the schoolbook answer comes out.
match the convention
Pick the method on purpose
Use round half up for homework, banker's rounding for finance and statistics, and ceiling or floor when you need a guaranteed direction (pricing tiers, container counts).
Lookup chart
Common numbers, already rounded
The quick answer to “what is X rounded to the nearest ten / hundred / thousand” without typing anything. All values use round half up.
NumberNearest 10Nearest 100Nearest 1,000
1,2341,2301,2001,000
1,8501,8501,9002,000
2,6752,6802,7003,000
3,4993,5003,5003,000
4,5004,5004,5005,000
5,0505,0505,1005,000
7,3217,3207,3007,000
9,8769,8809,90010,000
The same lookup for decimals — “X rounded to the nearest tenth / hundredth / thousandth”.
NumberTenthHundredthThousandth
3.141593.13.143.142
2.718282.72.722.718
1.414211.41.411.414
0.577350.60.580.577
9.806659.89.819.807
0.666670.70.670.667
FAQ
Common questions
Look at the thousandths digit — the third number after the decimal point. If it is 5 or more, add one to the hundredths digit; if it is 4 or less, leave it alone. Then drop everything after the second decimal place. For example, 3.14159 rounds to 3.14 because the deciding digit is 1.
Look at the tens digit. If it is 5 or more, round the hundreds digit up by one; if it is 4 or less, keep it. Replace the tens and ones with zeros. For example, 2847 has a tens digit of 4, so it rounds down to 2800; 2863 rounds up to 2900.
It depends on the method. Round half up — the everyday rule — sends 2.5 to 3. Round half down sends it to 2. Round half to even (banker's rounding) also sends it to 2, because 2 is the nearest even number. This calculator lets you switch between all of them.
Round half up is the standard rule taught in school: when the deciding digit is exactly 5, the kept digit rounds toward the larger value. So 0.5 becomes 1, 2.5 becomes 3, and 7.45 becomes 7.5. It is the default in this calculator.
Banker's rounding sends an exact half to the nearest even digit instead of always rounding up. So 2.5 becomes 2 and 3.5 becomes 4. Spreading ties evenly between up and down removes the slight upward bias that round half up introduces across many numbers, which is why finance and statistics prefer it.
Under round half up, the kept digit increases whenever the digit immediately to its right is 5, 6, 7, 8, or 9. If that deciding digit is 0, 1, 2, 3, or 4, the kept digit stays the same. That single test decides the result, no matter how many digits follow.
Round the magnitude as usual, then reattach the sign — for symmetric methods like round half up, −4.5 rounds to −5 and −2.3 rounds to −2. Ceiling and floor behave directionally: ceiling rounds toward positive infinity (so −4.5 becomes −4), while floor rounds toward negative infinity (so −4.5 becomes −5).
Rounding looks at the deciding digit and may bump the kept digit up. Truncating simply chops off the extra digits with no decision at all, always moving toward zero. So 3.99 rounds to 4 but truncates to 3.
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UC
Author
Ugo CharlesBuilt and fact-checked against our editorial standards · Last updated June 2026
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