Rounding Calculator Online
Round numbers to nearest integer, decimals, or place value using Half Up, Banker's Rounding, Ceil, and Floor.
Input Parameters
Live Result
Details
Steps
Input number: 149.995
Target place value: Hundredths (0.01)
Rounding mode: Half Up (Standard Math)
Scale factor applied: × 10^(2)
Computed rounded value: 150.00
Rounding deviation (Delta = Rounded - Original): +0.005
Quick Answer & Understanding Your Result
A Rounding Calculator adjusts numerical values to a simpler representation based on place value or significance: Standard Half-Up Rounding rounds halves (0.5) away from zero, while Banker's Rounding (Half Even, IEEE 754) rounds halves to the nearest even digit to eliminate cumulative statistical bias.
The 5 Standard Rounding Methods
- Half Up (Arithmetic): Traditional school rounding; halves (≥ 0.5) round away from zero (e.g., 2.5 → 3, -2.5 → -3).
- Half Even (Banker's): IEEE 754 standard; rounds to the nearest even number (2.5 → 2, 3.5 → 4) to neutralize rounding bias.
- Ceiling (Round Up): Rounds unconditionally toward positive infinity (e.g., 4.1 → 5, -4.9 → -4).
- Floor (Round Down): Rounds unconditionally toward negative infinity (e.g., 4.9 → 4, -4.1 → -5).
- Truncate (Drop): Drops all digits past the specified place value toward zero (e.g., 4.99 → 4).
Formula & Calculation Logic
Mathematical FormulaThe number is scaled by the target place value P, rounded according to the chosen algorithm rule, and then scaled back.
Step-by-Step Guide
Enter Target Number
Input the integer or decimal number you wish to round.
Select Place Value
Choose precision step: 1 for integer, 0.1 for tenths, 0.01 for hundredths, or 100 for hundreds.
Select Rounding Mode
Choose method: Half Up, Banker's Rounding (Half Even), Ceil, Floor, or Truncate.
Review Output & Delta
View the rounded value, difference error delta, and place value expansion.
Worked Examples Table
| Example | Input Values | Calculated Result | Explanation |
|---|---|---|---|
| Round 149.995 to Nearest Hundredth (0.01) | The thousandth digit is 5, causing hundredth 9 to roll over into 150.00. | ||
| Banker's Rounding for 2.5 and 3.5 | In Banker's rounding, .5 rounds to nearest even integer: 2 is even, 4 is even. | ||
| Ceiling Rounding for 83.2 | Ceiling always rounds upward to the next whole integer. |
Frequently Asked Questions
Evidence-Based Methodology & Authoritative References
IEEE 754 Standard for Floating-Point Arithmetic
NIST Reference on Constants, Units, and Uncertainty
Standard: ISO / W3C / IETF Authoritative Domain Standard
Formula: Half Up: round(x) = sign(x) × floor(|x| + 0.5)
Last Reviewed: August 21, 2026
Primary Source: IEEE 754 Standard for Floating-Point Arithmetic
Reference Document: NIST Reference on Constants, Units, and Uncertainty
Computation Privacy: 100% client-side 0ms computation, zero data retention
Calculated results are modeled based on standard scientific and mathematical formulas. Please verify with domain-specific technical documentation for specialized applications.
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Calculated results are modeled based on standard scientific and mathematical formulas. Please verify with domain-specific technical documentation for specialized applications.