Calculator Form
Enter a value, set an interval rule, and define a plotting range. Results appear above this form after submission.
Example Data Table
This sample uses interval size 0.5 and offset 0.
| x | floor(x) | ceiling(x) | Step floor | Step ceiling |
|---|---|---|---|---|
| -2.3 | -3 | -2 | -2.5 | -2.0 |
| -0.1 | -1 | 0 | -0.5 | 0.0 |
| 0 | 0 | 0 | 0.0 | 0.0 |
| 1.2 | 1 | 2 | 1.0 | 1.5 |
| 3.75 | 3 | 4 | 3.5 | 4.0 |
| 5.0 | 5 | 5 | 5.0 | 5.0 |
Formula Used
floor(x) = greatest integer less than or equal to x
ceiling(x) = least integer greater than or equal to x
step floor = a + h × floor((x - a) / h)Here,
h is interval size and a is offset.
step ceiling = a + h × ceil((x - a) / h)
fractional part = x - floor(x)
How to Use This Calculator
- Enter the target value in the Value x field.
- Set the Interval size h if you want step-based floor and ceiling boundaries.
- Use Offset a to shift the interval grid away from zero.
- Choose a plotting range using Range start, Range end, and Range step.
- Set Display precision to control decimal formatting.
- Click Calculate to show the results above the form.
- Review the summary, graph, and detailed table.
- Use the export buttons to download the results as CSV or PDF.
Frequently Asked Questions
1) What does the floor function return?
The floor function returns the greatest integer that is less than or equal to the input value. For example, floor(4.9) equals 4, and floor(-1.2) equals -2.
2) What does the ceiling function return?
The ceiling function returns the smallest integer that is greater than or equal to the input value. For example, ceiling(4.1) equals 5, and ceiling(-1.2) equals -1.
3) Why are floor and ceiling different for negative numbers?
Negative values often surprise learners because floor moves downward on the number line, while ceiling moves upward. For -2.3, the floor is -3 and the ceiling is -2.
4) What is the generalized step floor used for?
It helps round values down to custom intervals, not just integers. That is useful for pricing bands, measurement bins, inventory groupings, and chart bucket calculations.
5) What does the offset change?
The offset shifts the interval grid. With interval 0.5 and offset 0.25, valid step boundaries become 0.25, 0.75, 1.25, and so on.
6) Can floor and ceiling be equal?
Yes. They are equal whenever the input is already an integer. For example, if x equals 7, then both floor(x) and ceiling(x) equal 7.
7) What does the fractional part mean?
The fractional part shows how far the value is above its floor. It is calculated as x minus floor(x), which always falls between 0 and 1 for real numbers.
8) Why does this calculator include a graph and table?
The graph reveals step behavior across a range, and the table makes exact checks easier. Together, they help you study jumps, boundaries, and interval rounding patterns clearly.