Rounding Calculator

A rounding calculator (also called a round off calculator) trims a number to a chosen place using the round-half-up test: check the digit just right of your target; 5 or more rounds the place up, 4 or less leaves it. Round 3.14159 to two decimals and you get 3.14; round 754 to the nearest 100 and you get 800. Pick the place (decimal places, the nearest 10, 100 or 1,000, or a custom step) and the tie rule, and the answer plus the full reasoning appear instantly.

Need a different step? Choose Custom to round to any number of decimal places up to 30, or to the nearest multiple of any number: 0.05 for cash rounding to the nickel, 0.25 for quarter hours or quarter dollars, 0.125 for eighths, or 10,000 for big round figures. The same exact arithmetic is used, so a halfway case is always recognized as a tie.

A quick worked example

Take 3.14159 and round it to two decimal places. The digit in the second decimal place is 4 (3.14159). The digit just to its right is 1, which is below 5, so the 4 stays and everything after it is dropped. The result is 3.14, which is what the calculator shows when it opens. Now round 2.5 to a whole number: the deciding digit is exactly 5 with nothing after it, a true tie, so the rule matters. Round half up gives 3; banker's rounding (half to even) gives 2, because 2 is the even neighbor.

The rule in one line

For standard "round half up," the core test is the digit immediately right of your rounding place:

Written as a formula for rounding to a step s (where s = 0.01 for two decimals, or 10 for the nearest ten):

The calculator works in this "step space": it divides your number by the step, applies the chosen rounding rule to the result, then multiplies back. That single approach covers decimal places, the nearest 10, 100 or 1,000 and any custom multiple with the same logic, and because the division is done with exact whole numbers, a value that sits exactly halfway is never mistaken for one just below or above.

The seven rounding rules explained

• Round half up: the school default. A tie (…5) goes to the larger value. 2.5 → 3, 2.45 → 2.5, and -2.5 → -2.
• Round half down: a tie goes to the smaller value. 2.5 → 2, while 2.51 still rounds up to 3.
• Round half to even (banker's): a tie goes to the nearest even digit. 2.5 → 2, 3.5 → 4. This removes the upward bias of always rounding 0.5 up; it is the rule in NIST's guide to the SI, IEEE 754 floating-point arithmetic and Python's round().
• Round half away from zero: a tie moves away from zero, so 2.5 → 3 and -2.5 → -3. This is how Excel's ROUND function handles ties.
• Round up (ceiling): always move toward positive infinity, tie or not. 2.1 → 3, -2.1 → -2. Useful when you must never undershoot (buying enough material, sizing a container).
• Round down (floor): always move toward negative infinity. 2.9 → 2, -2.1 → -3.
• Truncate (toward zero): chop off the extra digits. 2.9 → 2, -2.9 → -2. For positive numbers this matches the floor; Excel's ROUNDDOWN works this way.

How to use this calculator

Three inputs, an instant result:

1. Number: type the value you want to round. Decimals, negatives and E-notation are fine; commas are ignored.
2. Round to: tap a target: a whole number, 1, 2 or 3 decimal places, the nearest 10, 100 or 1,000, or Custom for any number of decimal places or any multiple.
3. Rounding rule: choose how ties and directions are handled. Leave it on "round half up" for everyday rounding.

The big number at the top is your answer. Below it you get the original value, the exact adjustment rounding made, a plain-English explanation naming the two candidates on either side, and a table showing how all seven rules would round the same number, which is handy when a tie is involved.

Who this is for

• Students checking homework on decimal places, nearest ten, or estimation (rounding whole numbers and decimals to any place are Grade 4 and Grade 5 Common Core skills).
• Teachers demonstrating why 2.5 can become either 2 or 3 depending on the rule.
• Accountants and analysts who need banker's rounding to keep large sums unbiased, or whole-dollar rounding for tax forms.
• Engineers and scientists trimming measurements to a sensible precision before reporting them in scientific notation.
• Anyone estimating: rounding a bill, a budget, or a quantity to a round number in their head and verifying it.

Worked example 2: nearest 10, 100 and 1,000

Round 2,847 three ways. Nearest 10: the ones digit is 7 (≥ 5), so the tens round up: 2,847 → 2,850. Nearest 100: look at the tens digit, 4 (< 5), so it rounds down: 2,847 → 2,800. Nearest 1,000: look at the hundreds digit, 8 (≥ 5), so it rounds up: 2,847 → 3,000. Notice the answer can move in different directions depending on the place you round to; each place only "sees" the digits to its right.

Round to the nearest 10, 100, 1,000 and 10,000

The same number lands on different values at each place. These results use round half up; read across a row to see how a whole number collapses as the target place grows.

A number smaller than half the step rounds to 0: half of 10,000 is 5,000, so 754 becomes 0 at the nearest 10,000, yet it rounds up to 1,000 at the nearest 1,000 because 754 is more than half of 1,000. For 5,142,731 the nearest ten thousand is 5,140,000, because the deciding thousands digit is 2, which is below 5. Use Custom with a multiple of 10,000 or 100,000 to reproduce the last two columns.

Worked example 3: a tie under different rules

Round 0.125 to two decimal places. The third decimal is exactly 5 with nothing after it: a clean tie. Round half up gives 0.13. Round half down gives 0.12. Banker's rounding looks at the digit being kept (the 2), which is even, so the result stays 0.12. Same number, same place, three legitimate answers. This is exactly why financial and scientific work specifies the rounding rule up front.

Round decimals to the nearest tenth, hundredth and whole number

Common decimal roundings under the round-half-up rule. "Nearest tenth" means one decimal place; "nearest hundredth" means two. The calculator keeps trailing zeros so the place stays visible (2.99 to the nearest tenth is 3.0, not 3).

Note 0.207 to the nearest tenth is 0.2 (the hundredths digit 0 is below 5) and 3.74 to the nearest tenth is 3.7 (the hundredths digit 4 is below 5). The tie case 2.675 returns 2.68 because the tool works on the digits you typed, so 2.675 is an exact tie and round half up sends it up.

Reference: how a digit decides the round

For any single rounding place under the standard round-half-up rule, the digit immediately to the right decides the direction:

Rounding worked out step by step

Every round is the same three-step check: find the target place, read the single digit to its right, and go up if it is 5 or more. These examples use round half up.

Decimal places vs. significant figures

Decimal places count digits after the decimal point; significant figures count meaningful digits starting from the first non-zero one. They often disagree on small numbers. Rounded to two decimals, 0.04567 is 0.05 (one significant figure survives); rounded to two significant figures it is 0.046. This calculator handles decimal places and steps such as 10, 100 or 0.05; for sig-fig work, reach for the dedicated Significant Figures Calculator.

Tips for rounding well

• Round once, at the end. Carry full precision through a calculation and round only the final answer to avoid compounding errors.
• State your rule when results are shared: "rounded to the nearest cent, banker's rounding" removes ambiguity.
• Use ceiling for "enough" problems (materials, seats, servings) so you never come up short.
• Use banker's rounding for long sums to keep totals unbiased.
• Watch negatives: ceiling and floor move in opposite directions, so -2.5 can be -2 or -3 depending on the rule.

Why floating point sometimes "rounds wrong"

Computers store most numbers in binary, and many friendly-looking decimals (0.1, 2.675, 1.005) cannot be represented exactly. The stored value sits a hair above or below the decimal you typed, so a routine that rounds the stored value can flip the result: Python's documentation itself points out that round(2.675, 2) gives 2.67 instead of 2.68. This calculator sidesteps the problem entirely by doing the arithmetic on the decimal digits you typed, so genuine ties are always ties and non-ties are never mistaken for ties.

Related concepts and tools

Rounding sits next to a family of number-shaping tasks. If you are working with a percentage, round the percentage rather than the raw decimal; the Percentage Calculator keeps full precision until the end. To turn a long decimal into a clean fraction, use the Decimal to Fraction Calculator or the Fraction Calculator. For very large or very small numbers, scientific notation pairs naturally with significant-figure rounding. And when you round each value in a data set before taking an average, expect a small drift versus rounding the average itself, another reason to round last when you use the Average Calculator.

Where rounding shows up every day

Most rounding happens without anyone naming it. A few of the most common real-world places it matters:

• Money and tips. Currency is rounded to the nearest cent (two decimals), and many people round a restaurant bill to a whole dollar. When you split a check and add gratuity, the order of rounding can leave you a penny or two off, which is why a Tip Calculator should round the final share, not each step.
• Tax returns. IRS instructions allow whole-dollar amounts: drop amounts under 50 cents and raise 50 to 99 cents to the next dollar ($2.50 becomes $3), round every amount if you round any, and when a line adds several amounts, round only the total.
• Grades and scores. An 89.5% may round up to an A- or stay a B+ depending on whether the school uses round half up or rounds down: the same tie problem this tool illustrates. A GPA Calculator faces the same choice when converting weighted points.
• Measurements. A tape measure or scale already rounds to its smallest division; reporting more decimals than you measured implies false precision.
• Statistics and data. Survey percentages are usually rounded to whole numbers, which is why a pie chart's slices sometimes sum to 99% or 101% instead of exactly 100: a classic rounding artifact.
• Estimation and mental math. Rounding 47 + 28 to 50 + 30 = 80 gives a fast sanity check (the exact answer, 75, is close) before you trust a calculator's output.

A short history of why rounding rules differ

Round half up is old and intuitive: when in doubt, go bigger. But if every borderline value rounds up, a long column of figures drifts steadily upward, inflating totals. Round half to even (banker's rounding) cancels that bias by sending ties up half the time and down half the time, so errors average out near zero across many values. That is why NIST's guide to the SI gives it as the rule for rounding measured values, why IEEE 754 made it the default for binary floating-point arithmetic, and why Python's round() uses it. Excel's ROUND function, by contrast, rounds half away from zero, matching what most people learned in school. Neither rule is "wrong"; they answer different questions. Round half up is best for a single human-facing value; round half to even is best when you will sum or average thousands of rounded numbers.

Rounding direction at a glance

If you ever forget which rule moves a number which way, this table covers the borderline cases for both positive and negative inputs rounded to a whole number:

Two things stand out. The four "half" rules only differ on a true tie (2.5), never on a clear case like 2.4. And ceiling, floor and truncation ignore the halfway test entirely: they always push in a fixed direction, which is what makes them the right choice when you need a guaranteed minimum (ceiling) or maximum (floor) rather than the closest value.

How this calculator compares to a spreadsheet

Spreadsheet functions map onto the rules here, but the names and defaults trip people up. ROUND() in Excel and Google Sheets rounds half away from zero (so 2.5 → 3 and -2.5 → -3); Microsoft's own example is =ROUND(-1.475, 2) = -1.48. That matches this tool's "half away from zero" rule, and differs from "half up" only for negative ties. MROUND() rounds to the nearest multiple, the spreadsheet equivalent of the Custom multiple option here. ROUNDUP() and ROUNDDOWN() round away from and toward zero respectively, which is not the same as ceiling and floor for negatives. Python's built-in round(), meanwhile, uses banker's rounding. If a spreadsheet and this tool disagree on a tie, the cause is almost always a different rule: set both to the same rule and the numbers line up.

Sources & further reading

• NIST Special Publication 811, Appendix B.7.1, Rounding numbers (the round-half-to-even rule with worked examples).
• NIST, GLP 9, Rounding Expanded Uncertainties and Calibration Values (PDF) (even/odd rounding and "do not round intermediate calculations").
• Common Core State Standards: 4.NBT.A.3 (round multi-digit whole numbers to any place) and 5.NBT.A.4 (round decimals to any place).
• Internal Revenue Service, Instructions for Schedule D (Form 1040), "Rounding Off to Whole Dollars."
• Microsoft Support, ROUND function (with ROUNDUP, ROUNDDOWN and MROUND); Google Docs Editors Help, ROUND; Python documentation, round() (round half to even and the 2.675 example).
• IEEE 754-2019, Standard for Floating-Point Arithmetic, which makes round half to even the default rounding-direction attribute for binary arithmetic.