Input
Result
Original
—
Method
—
Rounded
—
Difference
—
Show steps
—
Calculation History
| # | Original | Method | Rounded | Difference |
|---|
Tip: Add computations to the table, then export to CSV or PDF.
Example Data Table
Use these examples to verify behavior across methods and signs.
| Amount | Method | Expect Rounded | Notes |
|---|---|---|---|
| 10.125 | half_even | 10.12 | Half to even: 1012.5 → 1012 is even |
| 10.125 | half_up | 10.13 | Half up: ties go up |
| 2.675 | half_even | 2.68 | 267.5 → 268 (even), beware binary pitfalls |
| -1.235 | half_even | -1.24 | Tie goes to even magnitude |
| -1.235 | half_up | -1.24 | Ties away from zero |
| 7.001 | truncate | 7.00 | Drop beyond two decimals |
| 7.001 | ceil | 7.01 | Ceiling at two decimals |
| -7.001 | floor | -7.01 | Floor goes more negative |
Formula Used
All nearest-cent operations work by scaling the number by 100, applying a rounding rule to the scaled value, then dividing by 100:
rounded = R( amount × 100 ) ÷ 100 Where R is one of: • Nearest, halves up: ties (…5) move away from zero. • Nearest, halves to even: ties go to the nearest even cent. • Ceiling at 2 decimals: always up (toward +∞) at the cent place. • Floor at 2 decimals: always down (toward −∞) at the cent place. • Truncate toward zero: drop digits beyond two decimals.
Implementation avoids binary floating issues by using string-based, integer scaling arithmetic before applying rules.
How to Use
- Enter the amount (commas allowed; negative values supported).
- Choose a rounding method that matches your policy.
- Set an optional currency symbol for display and exports.
- Click Compute to view the result and steps.
- Click Add to table for CSV/PDF export.
- Use the Example Data Table to verify expected behavior.
Rounding Methods Comparison
| Method | Rule Summary | Typical Use | Bias |
|---|---|---|---|
| Nearest, halves up | Ties (.005) away from zero | Retail invoices, receipts | Slight upward bias |
| Nearest, halves to even | Ties to even cent | Banking, financial ledgers | Low long‑term bias |
| Ceiling | Always up at the cent | Buyer‑protective pricing caps | Positive bias |
| Floor | Always down at the cent | Conservative accruals | Negative bias |
| Truncate | Drop beyond two decimals | Display‑only, interim steps | Toward zero |
Worked Examples (Cross‑Method)
| Amount | Half‑Even | Half‑Up | Ceil | Floor | Truncate |
|---|---|---|---|---|---|
| 10.125 | 10.12 | 10.13 | 10.13 | 10.12 | 10.12 |
| 2.675 | 2.68 | 2.68 | 2.68 | 2.67 | 2.67 |
| -1.235 | -1.24 | -1.24 | -1.23 | -1.24 | -1.23 |
| 7.001 | 7.00 | 7.00 | 7.01 | 7.00 | 7.00 |
| -7.001 | -7.00 | -7.00 | -7.00 | -7.01 | -7.00 |
Edge Cases & Validations
| Case | Why it matters | Expected Handling |
|---|---|---|
| .5 and -.5 | Inputs without a leading zero | Normalized to 0.50 and -0.50; ties handled per method |
| 2.675 | Binary fractions aren’t exact in base‑2 | String math yields 2.68 (half‑even/up), not 2.67 surprises |
| 1,234.567 | Thousands separators and 3+ decimals | Commas ignored; rounds to two decimals using selected rule |
| Invalid text | Robust form validation | Shows “Invalid amount” and prevents computation/export |
Scenario‑Based Policy Guide
| Scenario | Recommended Method | Notes |
|---|---|---|
| Bank ledger balancing | Nearest, halves to even | Reduces cumulative bias across many entries |
| Retail receipt totals | Nearest, halves up | Matches common point‑of‑sale behavior |
| Tax computations | Check local guidance | Jurisdictions differ; this tool supports both nearest rules |
| Accrual buffers | Floor | Conservative rounding on expenses/liabilities |
| Customer‑friendly pricing caps | Ceiling | Never under‑charge; rounds up at two decimals |
FAQs
It means rounding to exactly two decimal places (0.01 units) using a chosen rule such as halves up or halves to even.
Policies vary. Many finance systems use halves to even to reduce bias; invoices often use halves up. Match your accounting or regulatory guidance.
Yes. Rules are applied symmetrically with sign awareness. For example, ceiling increases negative numbers toward zero; floor moves them more negative.
Binary representations like 2.675 aren’t exact in base‑2, causing surprises. This tool does integer math on scaled decimal strings to stay exact.
Yes. Add each result to the table, then export as CSV or PDF for batch reconciliation.
No. Formatting may only display two decimals without changing the internal value. Rounding changes the numeric value according to the rule.
This tool targets two decimals. For zero‑decimal currencies, adapt the scale to 0 and use the same rules.