Rounding Calculator – Round to Decimal Places
Round any number to any number of decimal places with floor and ceiling options.
About This Calculator
Round any number to any number of decimal places with floor and ceiling options. Use the calculator above for instant results.
Rounding, Place Value, Floor, and Ceiling
Rounding replaces a number with a nearby value at a chosen place-value precision. To round to a specified decimal place, keep digits through that place and inspect the next digit. Under the common school rule for positive decimal numbers, a next digit of 5 or more increases the retained digit by one; a smaller next digit leaves it unchanged.
Rounding is different from truncation. Truncation discards later digits without asking which retained value is closer. Thus 7.389 truncated to two decimal places is 7.38, while ordinary rounding gives 7.39. Floor and ceiling are also directional operations rather than nearest-value rounding. The floor of a real number is the greatest integer not exceeding it, and the ceiling is the least integer not below it.
Negative numbers make directional language important. “Down” for floor means toward negative infinity, so floor(−2.3) = −3. Ceiling(−2.3) = −2. This differs from truncation toward zero. Tie-breaking at an exact halfway value can also vary by convention: school arithmetic often uses half-up or half-away-from-zero rules, while some statistical and programming systems use half-to-even to reduce aggregate bias.
Rounding should usually be delayed until the final step of a multi-step calculation. Repeatedly rounding intermediate values can accumulate error and shift the final result, especially in financial, statistical, and scientific computations.
Worked Examples
- Rounded: 3.14 | Floor: 3.14 | Ceiling: 3.15
Answer: 3.14
- Rounded: 3 | Floor: 2 | Ceiling: 3
Answer: 3
- Rounded: 1234.6 | Floor: 1234.5
Answer: 1234.6
Round 19.998 to two decimal places.
- The thousandths digit is 8, so 19.99 rounds upward.
Answer: 20.00
Rounding can carry across several 9s and change the integer part.
Consider −2.3.
- Floor = −3; ceiling = −2.
Answer: floor(−2.3)=−3, ceiling(−2.3)=−2
Floor moves toward negative infinity, not toward zero.
Who Uses This Calculator?
Round numbers for homework.
Round financial figures.
Significant figure rounding.
Floating-point rounding.
Common Mistakes to Avoid
❌ Rounding cascades
Round only the final answer in multi-step calculations.
❌ Decimal places vs sig figs
Decimal places: digits after decimal. Sig figs: total meaningful digits.
❌ Confusing floor with truncation for negative numbers
Truncating −2.8 toward zero gives −2, while floor(−2.8) is −3. The two operations agree for many positive values but not generally for negative values.
❌ Rounding every intermediate result
Carry extra digits through a calculation and round once at the requested final precision. Early rounding can accumulate enough error to alter the final reported digit.
Frequently Asked Questions
How to round?
Look at next digit: if >= 5, round up; if < 5, keep. 3.145 to 2dp = 3.15.
Truncating vs rounding?
Truncating removes digits without rounding. 3.149 truncated to 2dp = 3.14; rounded = 3.15.
Floor vs ceiling?
Floor: always round down. Ceiling: always round up. Rounding: goes to nearest.
What is rounding to significant figures?
Significant-figure rounding counts meaningful digits from the first nonzero digit rather than counting places after the decimal point. For example, 0.004567 rounded to three significant figures is 0.00457.
What is banker’s rounding?
Banker’s rounding commonly means round-half-to-even. At an exact halfway case, the retained last digit is made even. For example, 2.5 rounds to 2 and 3.5 rounds to 4 under that convention.
Why can decimal rounding behave unexpectedly in software?
Many decimal fractions cannot be represented exactly in binary floating-point. A stored value may be microscopically above or below the decimal you typed, which can affect a tie case. Financial software often uses decimal arithmetic or explicit rounding policies.
Does 20.00 mean the same value as 20?
Numerically they are equal, but written precision can carry information. In measurement contexts, 20.00 may indicate precision to the hundredths place, whereas 20 alone does not communicate the same measurement resolution.
Formula Explorer connections
Interpretation: This relationship converts, summarizes or checks numerical quantities using standard arithmetic and measurement rules. Assumption: Use consistent units, preserve enough significant digits, and round only the final result unless the method states otherwise.