Calculator
Enter your values below. The layout stays single column overall, while the inputs shift to 3, 2, and 1 columns by screen size.
Example Data Table
| Dividend | Divisor | Exact Quotient | Floor Quotient | Remainder |
|---|---|---|---|---|
| 27 | 4 | 6.75 | 6 | 3 |
| 17 | 5 | 3.4 | 3 | 2 |
| -17 | 5 | -3.4 | -4 | 3 |
| 17 | -5 | -3.4 | -4 | -3 |
| -17 | -5 | 3.4 | 3 | -2 |
These rows show how floor division differs from ordinary rounding and why signed divisors matter.
Formula Used
For dividend a and divisor b, where b ≠ 0, floor division uses the greatest whole value not larger than the exact quotient.
Meaning of the symbols
- q is the floor quotient.
- r is the remainder after using the floor quotient.
- floor means round downward to the next whole number.
How to Use This Calculator
- Enter a label if you want named exports.
- Type the dividend in the first numeric field.
- Type the divisor in the second numeric field.
- Choose how many decimal places you want displayed.
- Decide whether truncation comparison should appear.
- Select the graph style for the Plotly chart.
- Press Calculate Floor Division.
- Review the result card, chart, and optional export buttons.
FAQs
1) What is floor division?
Floor division divides one number by another, then rounds the quotient downward to the nearest whole number. The calculator also returns the remainder that satisfies a = b×q + r.
2) How is floor division different from regular division?
Regular division keeps the fractional part. Floor division removes that fraction by always rounding downward, not toward zero. Because of that rule, negative cases can produce different answers than truncation.
3) Why compare floor division with truncation?
The comparison shows whether rounding downward changed the quotient from the value you would get by dropping the fraction. This is especially useful for negative numbers, where the two methods often disagree.
4) What happens when the divisor is negative?
The quotient is still the floor of the exact result. The remainder adjusts so the identity a = b×q + r remains true. With a negative divisor, the remainder usually lands between the divisor and zero.
5) Can this calculator work with decimals?
Yes. The calculator accepts decimal inputs and still applies q = floor(a / b). The remainder is then computed from r = a - b×q, which keeps the identity valid for real values too.
6) When is the remainder zero?
The remainder becomes zero when the dividend fits the divisor exactly under the floor rule. In that case, the exact quotient is already a whole number, so floor division changes nothing.
7) Where is floor division used?
It is useful in modular arithmetic, indexing groups, bucket sizing, scheduling blocks, pagination, and algorithm design. It helps whenever you need complete groups and a leftover amount.
8) Why does the result card include an identity check?
The identity check confirms that the computed quotient and remainder rebuild the original dividend. It is a simple accuracy test and helps you verify tricky signed-number cases quickly.