Enter values to round
Calculation history
Formula used
The calculator first identifies the two neighboring integers. It compares the distance from the original value to each neighbor. The closer integer wins. A midpoint policy is needed only when both distances are equal.
For ordinary nearest-whole-number work, the default half-away-from-zero rule matches familiar classroom rounding: 6.5 becomes 7, while −6.5 becomes −7.
How to use this calculator
Enter a value
Type one decimal in the single-number field, or switch to batch rounding and paste many values.
Choose your rule
Keep the standard midpoint mode, or compare toward-zero, directional, even, and odd midpoint policies.
Calculate and review
Read the rounded value, direction, adjustment, errors, explanation, and number-line visualization.
Use advanced tools
Open the related-tools section for decimal places, positional places, significant figures, floor, ceiling, and truncation.
Export your work
Copy a single result, print the page, share supported links, or download batch output as CSV.
Review local history
Recent single calculations remain in this browser until you clear them or remove site storage.
Worked examples
The decimal part is below 0.5.
An exact midpoint moves away from zero.
The number is nearer to 8 than 7.
No rounding change is needed.
The value lies nearer to −4.
The standard tie rule moves away from zero.
The number lies nearer to zero.
The positive midpoint rounds to 1.
The negative midpoint rounds to −1.
Scientific notation is accepted when enabled.
Rounding, floor, ceiling, and truncation compared
Nearest rounding
Chooses the target with the smallest distance. For 8.75, nearest whole gives 9. For −8.75, it gives −9.
Floor
Moves toward negative infinity. Floor(8.75) is 8, while floor(−8.75) is −9.
Ceiling
Moves toward positive infinity. Ceiling(8.25) is 9, while ceiling(−8.25) is −8.
Truncation
Removes the fractional portion and moves toward zero. Truncating 8.99 gives 8, and truncating −8.99 gives −8.
Understanding nearest-whole-number rounding
Why rounding is useful
Rounding replaces a detailed number with a simpler nearby value. It makes measurements easier to communicate, estimates faster to compare, and reports less cluttered. A store might summarize 18.67 kilograms as 19 kilograms when only whole kilograms matter. A class may report 84.2 students as about 84 students for an average, even though a literal fraction of a student is impossible. The important point is that rounding changes presentation and precision; it does not improve the accuracy of the original measurement.
Finding the neighboring integers
Every non-integer decimal lies between two consecutive integers. The number 18.67 lies between 18 and 19. Its distance from 18 is 0.67, while its distance from 19 is 0.33. Because 0.33 is smaller, 19 is the nearest whole number. Negative values follow the same distance principle. The number −4.49 lies between −5 and −4. It is 0.49 from −4 and 0.51 from −5, so −4 is closer.
The special midpoint case
A value ending exactly in one-half is equally distant from two integers. For example, 6.5 is 0.5 from both 6 and 7. A tie-breaking convention is therefore required. Elementary lessons commonly use half away from zero, which sends 6.5 to 7 and −6.5 to −7. Financial, statistical, and technical systems may use half to even because repeated ties can otherwise push totals consistently in one direction. This calculator makes the selected convention visible instead of silently assuming every context uses the same one.
Rounding negative values correctly
Words such as “up” and “down” can cause mistakes with negative numbers. On a number line, −3 is greater than −4, so moving toward −3 is movement toward positive infinity. Standard half-away rounding sends −3.5 to −4, which is numerically downward but farther from zero. For that reason, the clearest method is to compare distances and then apply a named midpoint policy only when necessary.
Error and responsible use
The absolute rounding error is the distance between the original and rounded values. Rounding 18.67 to 19 creates an absolute error of 0.33. Percentage error divides that distance by the magnitude of the original value and multiplies by 100. Percentage error is undefined when the original value is zero. Avoid rounding intermediate values too early in a long calculation because small changes can accumulate. Keep extra precision during the work, then round the final result to the level required by the situation.
Frequently asked questions
What is a whole number?
A whole number has no fractional or decimal portion. In elementary usage, whole numbers are 0, 1, 2, 3, and so forth. This calculator also rounds negative decimals to integers.
What happens when the decimal part is below 0.5?
The value moves to the nearer lower-magnitude or adjacent integer. For example, 12.24 rounds to 12, while −12.24 rounds to −12.
What happens when the decimal part is exactly 0.5?
The selected midpoint policy decides the result. The default policy is half away from zero, so 3.5 becomes 4 and −3.5 becomes −4.
Is rounding the same as truncation?
No. Rounding chooses a nearby target according to distance. Truncation simply removes digits after the decimal point, so 8.99 truncates to 8 but rounds to 9.
Why do negative numbers seem different?
They are not different in distance. The words up and down can be confusing because −5 is below −4. The result cards show both direction and signed adjustment.
What is half to even?
Half to even sends an exact midpoint to the neighboring even integer. Thus 2.5 becomes 2, 3.5 becomes 4, and −2.5 becomes −2. It can reduce cumulative bias.
What is half to odd?
Half to odd sends an exact midpoint to the neighboring odd integer. Thus 2.5 becomes 3 and 3.5 becomes 3. It is less common but useful for comparison.
What does half up mean here?
In this calculator, an exact midpoint moves toward positive infinity. Therefore 2.5 becomes 3 and −2.5 becomes −2. The label states this direction explicitly.
What does half down mean here?
In this calculator, an exact midpoint moves toward negative infinity. Therefore 2.5 becomes 2 and −2.5 becomes −3.
Can I enter scientific notation?
Yes. Keep the scientific-notation option enabled and enter values such as 1.75e3, 6.02e2, or −4.2E−3 using a standard keyboard minus sign.
Can I use a comma as the decimal separator?
Yes. Select comma decimal input. In that mode, use line breaks, spaces, semicolons, or tabs between batch values because commas belong inside numbers.
How many batch values can I calculate?
The server-side form accepts up to 1,000 values per submission. This limit keeps rendering and browser interaction responsive on typical devices.
Why is percentage error unavailable for zero?
Percentage error divides by the magnitude of the original value. Division by zero is undefined, so the calculator displays “Not defined” for an original value of zero.
Does the calculator store my numbers on a server?
No database is used. A normal form submission is processed by the current PHP request. Optional history is saved only in your browser local storage.
Can I round to a tenth or hundredth?
Yes. Open Related rounding tools and choose the desired operation. The main default remains nearest whole number.
Can I calculate floor and ceiling values?
Yes. Floor chooses the greatest integer not exceeding the input. Ceiling chooses the smallest integer not below the input.
What are significant figures?
Significant figures count meaningful digits from the first nonzero digit. This page can round a value to between one and fifteen significant figures.
Why can floating-point results look unusual?
Computers store many decimals as binary approximations. The calculator uses tolerance-aware midpoint checks and cleans insignificant display zeroes, but extreme values still follow finite floating-point limits.
Can I copy or download results?
Yes. Single results can be copied or shared. Batch results can be copied as tab-separated text or downloaded as a CSV file.
Will the page work without JavaScript?
Yes. The PHP form performs calculations after submission. JavaScript adds instant preview, tabs, history, copying, CSV export, theme selection, and number-line interaction.