Rounding Calculator
Round any number to the nearest 10, 100, 1000, 5, decimal place or significant figure. See which digit decides, plus half up, half even and bankers rounding.
The number you want to round
What happens to the value in between landmarks; the half rules differ only on an exact half
Results
Rounded Value
70
- Original Number
- 74
- Rounding Direction
- Round Down
- Rounding Rule
- Half away from zero (standard)
- Why
- The first dropped digit is 4, less than 5, so the value is below the midpoint 75: it rounds to 70.
The formula
round(x) = floor(x / step + 0.5) × step
- x
- Original Number
- step
- Rounding Step
- Deciding digit
- Digit Right of the Place
Worked example — Number to Round 74, Multiple 25, Significant figures 3
Rounded Value = 70
How Rounding Calculator Works
round(x) = floor(x / step + 0.5) × step
Rounding replaces a number with a nearby value that is shorter, simpler, or more explicit. To round to a place value, find that place, then look at the digit immediately to its right: the deciding digit. If the deciding digit is 5 or more, the digit in the rounding place goes up by 1; if it is 4 or less, it stays. Every digit after the rounding place becomes a zero (or is dropped after the decimal point).
For example, 74 rounded to the nearest ten: the deciding digit is the ones digit 4, which is less than 5, so 74 → 70. To round to a multiple (nearest 5, 25, 0.05), divide by the step, round to a whole number, then multiply back.
- x
- Original Number — The number to be rounded. Can be any real number including integers, decimals, or negative numbers.
- step
- Rounding Step — The size of the grid you round to: 1,000,000 down to 0.0001 for a place value, 5 for "nearest 5", or any positive number you type for "nearest multiple of".
- Deciding digit
- Digit Right of the Place — The first digit that is dropped. For place values it decides the direction: 5 to 9 rounds up, 0 to 4 stays. The calculator highlights it in your number.
Worked Examples
Round 1,267 to the nearest hundred for a budget estimate.
number = 1267 · place = hundred
1,300
The hundreds digit is 2, and the tens digit is 6. Since 6 ≥ 5, we round up. The hundreds digit increases from 2 to 3: 1,267 → 1,300. All digits after the hundreds place become zeros.
Round 3.14159 to the nearest hundredth for π approximation.
number = 3.14159 · place = hundredth
3.14
The hundredths digit is 4, and the thousandths digit is 1. Since 1 < 5, we round down to 3.14. This is the classic two-decimal approximation of π used in basic calculations.
Round 74.5 to the nearest unit (whole number) to test the midpoint rule.
number = 74.5 · place = unit
75
The number 74.5 is exactly at the midpoint between 74 and 75. The default rule (exact halves round away from zero) gives 74.5 → 75. Banker's rounding would round to 74 (nearest even number) instead.
Round 8,421 to the nearest thousand.
number = 8421 · place = thousand
8,000
The thousands digit is 8 and the deciding digit is the hundreds digit, 4. Since 4 < 5 the thousands digit stays: 8,421 → 8,000. Compare 8,521, which rounds up to 9,000.
Round 48 to the nearest 5 to pick a standard size.
number = 48 · place = five
50
48 lies between 45 and 50. The midpoint is 47.5 and 48 is above it, so it rounds up to 50. A number such as 42 is below the midpoint 42.5 and rounds down to 40.
Round 4.37 to the nearest 0.05, as some cash systems do.
number = 4.37 · place = multiple · multiple = 0.05
4.35
4.37 lies between 4.35 and 4.40. The midpoint is 4.375, so 4.37 rounds down to 4.35.
Round 0.004567 to 2 significant figures.
number = 0.004567 · place = sig · sigFigs = 2
0.0046
Leading zeros do not count. The first significant figure is the 4, the second is the 5, and the deciding digit is the 6, which rounds the 5 up: 0.004567 → 0.0046.
Round 2.5 to a whole number with banker's rounding.
number = 2.5 · place = unit · method = half-even
2
2.5 is exactly halfway between 2 and 3. Half to even picks the even neighbour, 2. 3.5 would go up to 4, also the even neighbour. Half up gives 3 for 2.5.
Understanding the Result
Rounding is a fundamental estimation skill used daily in finance (rounding prices and taxes), statistics (reporting significant figures), engineering (tolerances), and everyday life (estimating costs). The number line helps learners see that rounding means finding which "landmark" value the original number is closest to. For example, 74 is between 70 and 80 on the number line, and since 74 is less than 75 (the exact midpoint), it rounds down to 70.
If the number were 75, the usual school convention is to round up to 80 (known as "round half up", the most common rounding method). The midpoint rule is a convention, not a mathematical truth, which is why several rules exist: "round half to even" (banker's rounding) sends an exact half to the nearest even digit so that halves do not always move the same way, "round half down" sends it toward zero, and "round toward zero" (truncation) simply discards the extra digits, as integer division does in many programming languages.
The half rules only disagree on an exact tie such as 2.5 or 15 to the nearest ten; for any other number they give the same answer. The always-up, always-down and truncate rules never look at the midpoint at all.
How to Use
- Enter the number you want to round in the input field.
- Choose what to round to: a place value (nearest ten, hundred, thousand, tenth, hundredth…), the nearest 5, the nearest multiple of any number you type, or a number of significant figures.
- Choose a rounding rule. The standard school rule (half away from zero) is the default; half down, banker's half-to-even, always up, always down and truncate are in the menu.
- Read the result, the digit-by-digit explanation of which digit decided, the number line, and the tables that show the same number under every rule and at every place value.
Quick Reference
| Nearest ten | 74 → 70 (look at the ones digit) |
| Nearest hundred | 1,250 → 1,300 (look at the tens digit) |
| Nearest thousand | 8,421 → 8,000 (look at the hundreds digit) |
| Nearest 5 | 48 → 50, 42 → 40 |
| Nearest whole number | 3.6 → 4 |
| Nearest tenth | 3.72 → 3.7 (1 decimal place) |
| Nearest hundredth | 3.728 → 3.73 (2 decimal places) |
| Significant figures | 0.004567 to 2 s.f. → 0.0046 |
| Half up (standard) | 2.5 → 3, −2.5 → -3 |
| Half down | 2.5 → 2, −2.5 → -2 |
| Banker's (half to even) | 2.5 → 2, 3.5 → 4 |
| Always up / always down | 2.1 → 3 / 2; −2.1 → -2 / -3 |
| Truncate (toward zero) | 2.9 → 2, −2.9 → -2 |
Frequently Asked Questions
- How do you round numbers?
- Pick the place you are rounding to, look at the digit immediately to its right (the deciding digit), and decide: 5, 6, 7, 8 or 9 means the digit in your place goes up by 1; 0, 1, 2, 3 or 4 means it stays. Then replace every digit after your place with zeros (for whole numbers) or drop them (after the decimal point). For example, 74 to the nearest ten: the deciding digit is 4, so it stays and 74 → 70. Enter any number above and the calculator highlights the deciding digit for you.
- How do you round to the nearest ten?
- Look at the ones digit. If it is 5 or more, round up to the next ten; if it is 4 or less, round down to the ten below. 74 → 70, 76 → 80, and 75 → 80 under the standard rule because 75 is exactly halfway. Choose "Nearest Ten" in the Round to menu.
- How do you round to the nearest hundred?
- Look at the tens digit. If it is 5 or greater, round the hundreds digit up; if it is 4 or less, keep it. Digits after the hundreds place become zeros. 1,250 rounds to 1,300 (tens digit 5) and 1,249 rounds to 1,200 (tens digit 4).
- How do you round to the nearest thousand?
- Look at the hundreds digit. 5 or more rounds the thousands digit up, 4 or less leaves it. 8,421 → 8,000 and 8,500 → 9,000. Digits after the thousands place become zeros.
- What is rounding to the nearest tenth?
- Rounding to the nearest tenth keeps one decimal place. Look at the hundredths digit (second decimal place). For example, 3.72 rounded to the nearest tenth is 3.7 (the hundredths digit 2 is less than 5). If the number were 3.78, it would round to 3.8. The same idea gives the nearest hundredth (two decimal places, look at the thousandths digit) and the nearest thousandth.
- Does 0.5 round up or down?
- With the standard school rule, 0.5 rounds up to 1 (and −0.5 rounds to -1, away from zero). But 0.5 is exactly halfway between 0 and 1, so other conventions differ: half down and banker's rounding (half to even) both give 0. Use the "Rounding rule" menu to see each, or read the table of every rule under the result.
- What is bankers' rounding and how is it different?
- Bankers' rounding (also called round half to even) rounds an exact half to the nearest even number instead of always rounding away from zero. So 2.5 → 2, 3.5 → 4, 4.5 → 4. Because halves go up about as often as they go down, it avoids the systematic upward drift of always rounding halves up, which is why it is used in some accounting and software settings. Choose it in the Rounding rule menu; it only differs from the standard rule on exact halves.
- What is the difference between round half up, half down and half to even?
- They only differ on an exact tie. For 2.5 to a whole number: half up gives 3, half down gives 2, half to even gives 2. For 3.5: 4, 3 and 4. Any number that is not exactly halfway rounds to the same value under all three.
- How do you round to significant figures?
- Count from the first non-zero digit (leading zeros never count), keep the number of digits you asked for, and use the next digit to decide. 0.004567 to 2 significant figures is 0.0046, and 123,456 to 3 significant figures is 123,000. Trailing zeros after the decimal point are kept because they are significant: 1.2 to 3 significant figures is 1.20. Choose "Significant figures" in the Round to menu and type how many to keep.
- How do you round to the nearest 5?
- Find the two multiples of 5 on either side of your number and pick the closer one. 48 is between 45 and 50 and closer to 50, so it rounds to 50; 42 is closer to 40, so it rounds to 40. A number halfway between, such as 42.5, goes to 45 under the standard rule. Choose "Nearest 5", or "Nearest multiple of…" for 25, 50 or 0.05.
- What is the difference between rounding, rounding up and rounding down?
- Plain rounding goes to the nearest landmark, using the deciding digit. "Round up" (ceiling) always moves to the larger neighbour and "round down" (floor) always to the smaller one, whatever the next digit is: 2.1 rounds up to 3 and down to 2. Truncating discards digits and moves toward zero, so −2.9 truncates to -2 while rounding down gives -3.
- How does rounding affect negative numbers?
- With the standard rule, a negative number is rounded by its size, then given its sign back: −3.4 rounds to -3 and −3.6 rounds to -4, and the tie −3.5 goes to -4 (away from zero). Some programming languages treat negative ties differently — JavaScript's Math.round(−3.5) gives −3 — so check the rule of your own tool.
- Why does 1.005 round to 1.01 here when other tools show 1.00?
- This calculator works on the exact decimal digits you type, so 1.005 is exactly halfway between 1.00 and 1.01 and the standard rule gives 1.01. Many programs store 1.005 as a binary floating-point number that is slightly below 1.005, so they print 1.00 instead. Neither tool is "wrong"; they are rounding different values.
Pro Tips
- →When rounding for financial estimates, round to two decimal places (nearest hundredth) for dollar amounts — this matches the cent precision of real currency.
- →The number of decimal places you keep signals your measurement precision. A measurement of 3.140 m implies precision to the nearest millimeter, while 3.14 m implies precision to the nearest centimeter.
- →When rounding a series of numbers for a total, round AFTER summing, not before. Rounding each term individually can accumulate errors. For example, 1.4 + 1.4 + 1.4 = 4.2, which rounds to 4, but rounding each term first gives 1 + 1 + 1 = 3.
- →For scientific work, consider using significant figures instead of fixed decimal places. Significant figures convey both the value and the precision: 0.050 has two significant figures (the leading zeros do not count), while 0.0500 has three.
- →If two tools disagree on a number like 2.5 or 0.125, they are probably using different tie rules. Compare them with the "same number under every rule" table under the result.
Limitations to Know
- •The default rule is the standard school convention: exact halves round away from zero (2.5 → 3, −2.5 → −3). Half down, banker's rounding (half to even), always-up, always-down and truncation are available in the "Rounding rule" menu; half to odd and stochastic rounding are not.
- •Negative numbers follow the same digit rule on their magnitude: -3.5 rounds to -4 (not -3) under the default rule. Some tools differ (JavaScript Math.round gives -3; Python round() rounds half to even, so round(-2.5) is -2), so check the rule when comparing.
- •Place values run from the nearest million down to the ten-thousandth; for anything else choose significant figures (1 to 30) or the nearest multiple of any positive number. The arithmetic is exact on the digits you type (up to 100 digits), so 1.005 correctly rounds to 1.01 at the hundredth.
- •Rounding to a multiple has no "deciding digit": the calculator compares your number with the midpoint between the two neighbouring multiples instead.
Cite this calculator
TheCalcUniverse. "Rounding Calculator: Nearest 10, 100, Decimals, Sig Figs." TheCalcUniverse, 2026, https://thecalcuniverse.com/math/rounding-calculator/. Accessed October 25, 2026.
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