Test any number with instant Kaprekar verification. See square splits, range matches, graphs, and exports. Practice confidently using examples, formulas, FAQs, and clear guidance.
Enter one number for checking and a range for discovery. Results appear above this form after submission.
The graph shows Kaprekar numbers found in your chosen range. When no range hits appear, it shows the current split components instead.
Let n be a positive integer with d digits.
Square the number: s = n²
Split point: 10^d
Right part: r = s mod 10^d
Left part: l = floor(s / 10^d)
Kaprekar rule: l + r = n, with r > 0, while 1 is treated as valid.
Example for 45:
45² = 2025
Split into 20 and 25.
20 + 25 = 45, so 45 is a Kaprekar number.
| Number | Square | Left Part | Right Part | Left + Right | Kaprekar? |
|---|---|---|---|---|---|
| 1 | 1 | 0 | 1 | 1 | Yes |
| 9 | 81 | 8 | 1 | 9 | Yes |
| 10 | 100 | 10 | 0 | 10 | No |
| 45 | 2025 | 20 | 25 | 45 | Yes |
| 55 | 3025 | 30 | 25 | 55 | Yes |
| 99 | 9801 | 98 | 1 | 99 | Yes |
| 297 | 88209 | 88 | 209 | 297 | Yes |
| 703 | 494209 | 494 | 209 | 703 | Yes |
A Kaprekar number is a positive integer whose square can be split into two parts that add back to the original number. The split uses the digit count of the original number.
For 1, the square is 1. Splitting it gives left part 0 and right part 1. Their sum is 1, so it satisfies the Kaprekar condition.
The square of 10 is 100. Using two digits, the split becomes 10 and 0. Many standard definitions reject a zero right part, so 10 is not counted here.
Yes. It scans every integer in the selected interval, tests each one with the Kaprekar rule, and builds a table of valid matches found in that range.
The graph plots Kaprekar numbers discovered in the selected range against their squares. If none are found, it switches to a component chart for the checked number.
Very large scans can slow browser rendering and server processing. The built-in limit keeps the page responsive while still supporting broad searches for classroom or practice use.
Square the number, split the square using the original digit count, then add the left and right parts. If that sum equals the original number, it is Kaprekar.
Yes. The calculator includes CSV and PDF export buttons, so you can download the current result summary and range analysis for reports, assignments, or notes.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.