How this calculator works
Rounding to a place value replaces the digits below that place with zeros and changes the digit at the place according to a rule. To round to the nearest thousand, look at the hundreds digit and the digits after it. Ordinary half-up rounding sends anything below 500 down and anything from 500 upwards up. The other rules answer the awkward exactly-half cases differently, which matters in finance, engineering and statistics.
Formula
Divide the number by the place value, apply the chosen rule at the half point, then multiply back. For half-up: nearest thousand = sign(x) × floor(|x|/1000 + 0.5) × 1000.
Worked example
With half-up rounding, 3,456 becomes 3,000, while 3,500 becomes 4,000. The same number rounded to the nearest ten thousand is 0 and to the nearest hundred thousand is 0. A value of 45,678 becomes 46,000, 50,000 and 0 respectively.
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Frequently asked questions
Which rounding rule should I use?
Half-up is the everyday default in schools and most business arithmetic. Half-even, also called banker's rounding, avoids a systematic upward bias and is used in many accounting and statistical systems. Ceiling and floor are for cases where you must never under- or over-state a value.
What is the difference between up and ceiling?
Up moves away from zero, so -1,200 rounds up to -2,000. Ceiling moves toward plus infinity, so -1,200 rounds to -1,000. They agree for positive numbers and differ for negative ones.
Why do the three outputs disagree with each other?
They round to different place values, so they answer different questions. A number can round to 46,000 at the thousand place and to 0 at the hundred-thousand place in the same step.
Does this round to significant figures instead?
No. This page rounds to fixed place values, so the number of zeros is fixed. To keep a fixed count of significant digits, use the significant figures tool.