Calculator Form
Use decimals, choose a quotient rule, and control display precision.
Example Data Table
| Dividend | Divisor | Mode | Remainder | Why It Matters |
|---|---|---|---|---|
| 17.45 | 2.80 | Euclidean | 0.65 | Keeps the remainder non-negative. |
| -17.45 | 2.80 | Truncated | -0.65 | Matches truncation toward zero. |
| -17.45 | 2.80 | Floor-Based | 2.15 | Uses the floor of the quotient. |
| 9.60 | 0.40 | Euclidean | 0.00 | Shows exact decimal divisibility. |
Formula Used
The calculator applies the general remainder identity r = a - d × q. Here, a is the dividend, d is the divisor, and q is the selected integer quotient.
- Euclidean mode: picks a quotient that keeps 0 ≤ r < |d|.
- Truncated mode: uses quotient truncation toward zero, so the remainder follows the dividend sign.
- Floor-based mode: uses floor(a / d), which changes results for negative values.
The remainder ratio shown on the page is |r| / |d|. It helps compare the leftover part against the divisor size.
How to Use This Calculator
- Enter the decimal dividend you want to divide.
- Enter a non-zero decimal divisor.
- Select Euclidean, truncated, or floor-based remainder mode.
- Choose the number of decimal places for display.
- Press Calculate Remainder to show the result above the form.
- Review quotient, lower multiple, and exact division status.
- Use the CSV or PDF buttons to export the saved results.
Recent Calculation History
No calculations yet. Run the form once to build exportable history.
FAQs
1. What is a decimal remainder?
A decimal remainder is the leftover amount after division when values contain decimal places. It depends on the quotient rule used, especially when negative numbers are involved.
2. Why do different modes give different answers?
Each mode chooses the integer quotient differently. Truncated mode cuts toward zero, floor-based mode rounds downward, and Euclidean mode forces a non-negative remainder.
3. When should I use Euclidean mode?
Use Euclidean mode when you want the remainder to stay between zero and the divisor magnitude. It is common in mathematical definitions and modular arithmetic workflows.
4. What does lower multiple mean here?
Lower multiple is the portion exactly divisible by the divisor after removing the remainder. It helps confirm that dividend equals lower multiple plus remainder.
5. Why can a remainder be negative?
Negative remainders appear in truncated mode when the dividend is negative. The result follows the dividend sign because the quotient is truncated toward zero.
6. Does the calculator support exact divisibility checks?
Yes. The exact division field reports whether the calculated remainder is effectively zero at the selected display precision, which is useful for validation and QA checks.
7. What is exported in CSV and PDF files?
The exported files include the saved calculation history. They capture dividend, divisor, mode, quotient, remainder, lower multiple, remainder ratio, and exact division status.
8. Is this calculator suitable for negative divisors?
Yes. Negative divisors are accepted. Mode selection matters, because sign behavior changes with floor-based and truncated rules while Euclidean mode keeps the remainder non-negative.