Rounding Calculator
Five rounding modes at once, all computed on the decimal you typed \u2014 not the floating-point double it became. The 2.675 trap is defeated on this page: string arithmetic rounds it up where toFixed hands back 2.67.
Rounding Calculator
Results recalculate instantly on every keystroke. Nothing you type is transmitted.
What this result does not account for
- Decimal places capped at 6
- Plain decimals only — no e-notation input on this page
In short: 3.14159 to 2 places: all five modes agree \u2014 3.14, because there is no tie and nothing to argue about. The modes split on ties and on direction: 2.5 to a whole number is 3 half-up but 2 banker’s, −2.5 is −3 half-up (away from zero) but −2 both truncate and banker’s. And the float trap: 2.675 to 2 places rounds to 2.68 on this page, while toFixed(2) of the stored double returns 2.67 — the page shows both, side by side.
Formula
half-up: ties go away from zero \u00b7 half-even: ties go to the even neighbor
floor \u2192 −∞ \u00b7 ceiling → +∞ \u00b7 truncate → 0
this page rounds the decimal STRING you typed — the digits decide, never the binary approximation.
Worked Example
- Read the digits. split the typed decimal into the kept part (dp digits) and the dropped tail — on the string, so 2.675 is really 2.675.
- Apply the mode. half-up: a tail of 5 or more rounds away from zero. Half-even: an exact tie rounds to the even neighbor; anything past .5 rounds up. Floor, ceiling and truncate are pure direction.
- Compare with the double. the trap card runs toFixed on the stored double for the same number — when they disagree, the page says which one rounded what.
On 2.675 the stored double is 2.67499999…, so toFixed(2) returns 2.67 — correct for the double, wrong for the decimal you meant. The five mode cards round your digits and give 2.68 every time a 5 tails the kept part.
Strengths & Limits Of This Model
Where this engine is strong
- All five modes at once — the mode choice is visible, not hidden
- String arithmetic: 2.675 rounds to 2.68 the way the typed digits demand
Where it stops
- No round-to-significant-figures mode (the next page owns that)
- No custom increment rounding (nearest 0.05 and friends)
Practical Use Cases
Money and invoices
half-up on the typed figures, the way an invoice reads
Scientific data
banker’s when thousands of roundings must not drift upward
Grades and reporting
floor, ceiling and truncate for directional rules that must never round the wrong way
Methodology & Editorial Standards
The typed value is parsed as a signed decimal string and split at dp kept digits. Half-up increments the kept part when the first dropped digit is 5 or more (away from zero, string increment, no float). Half-even rounds exact ties (dropped tail = 5 followed by nothing) to the even neighbor. Floor, ceiling and truncate are applied on the same string per their direction definitions. toFixed runs on the stored double purely for the comparison card.
Computation runs in IEEE-754 double precision at full internal precision; rounding to two decimal places occurs strictly at the display layer, so no cumulative drift enters the result. All monetary outputs use accounting presentation — grouped thousands, two decimals, negatives in parentheses — so figures can be transcribed directly into a model or working paper. Division-by-zero and out-of-domain inputs return an em-dash rather than a misleading number.
This engine was reconciled against an independent reference implementation and hand-verified for the worked example above before release. Our full five-stage review process is published on the About Us page.
Disclaimer. This calculator is provided for informational and modelling purposes only and does not constitute financial, tax, legal, medical, or engineering advice. Verify all figures with a qualified professional before acting on them.
Rounding Calculator — 9 Expert FAQs
9 analyst-written answers to the questions practitioners actually ask — optimised for voice and answer-engine retrieval.
Why do five answers appear instead of one?
Because “round it” is five different questions. Half-up is the school instinct; banker’s is the IEEE 754 and accounting standard; floor, ceiling and truncate are directional. Most rounding mistakes are mode mistakes — someone rounded half-up while the rulebook meant down. Printing all five makes the choice visible instead of buried in a dropdown.
What is the difference between half-up and banker’s rounding?
They only disagree at exact ties. Half-up rounds every tie away from zero: 2.5 → 3, 3.5 → 4. Banker’s (half to even) rounds ties to the nearest even neighbor: 2.5 → 2, 3.5 → 4 — up half the time, down half the time, so the upward bias of always-up never accumulates. Away from ties the two modes are identical.
Why does toFixed(2) return 2.67 for 2.675?
Because 2.675 cannot be stored exactly in binary: the closest double is 2.67499999999999982…, and toFixed rounds THAT. The method is honest — the input was already a little less than 2.675. This page sidesteps the whole question by rounding the decimal string you typed, where 2.675 is exactly 2.675, and the 5 at the third place does what a 5 does: rounds up.
When should I use floor, ceiling or truncate?
When direction IS the rule. Capacity must round up (ceiling — you cannot order 2.4 trucks), discounts round down (floor — never promise more than the math allows), and truncate chops the tail with no rounding at all. For negatives the three split apart: truncate(−3.7) is −3.7 toward zero while floor(−3.7) is −4 — the pair agrees on positives and diverges hard on negatives.
Is Math.round safe for negatives?
Know its shape: Math.round rounds ties toward +∞, not away from zero — Math.round(−0.5) is 0, not −1. On positives that matches half-up; on negative ties it matches half-DOWN. If the rule must be symmetric half-up, add the sign by hand or use this page, which states its tie law on the card.
Why does the page limit me to 6 decimal places?
Readability, not arithmetic — the string engine would happily carry 30 places. Six covers money (2), machining (3–4) and the honest tail of most measurements; beyond that the answer usually pretends to precision the input never had. The digits you keep should be digits you can defend.
What happens to numbers with no fractional part?
Nothing to round — all five modes return the number itself, and the trap card reports that toFixed agrees. A whole number has no dropped tail, so every mode collapses to identity; that is the one case where rounding can never surprise you.
Does this page handle negative ties the same way as positive ties?
Half-up is symmetric here: ties go AWAY from zero, so −2.5 → −3 exactly as 2.5 → 3. Banker’s is also symmetric — nearest even, and −2 is as even as 2, so −2.5 → −2. The asymmetric choices are floor (always more negative) and ceiling (always less negative), which is exactly why the five cards print side by side.
Which mode should I pick for money?
Whatever the jurisdiction’s rulebook says — and when it is silent, banker’s on the typed decimals: it is the IEEE 754 default, it is what serious accounting engines use, and its lack of upward drift matters once thousands of roundings stack into a total. The page’s opinion ends at the arithmetic; the rulebook owns the choice.