Turn any number into one digit using smart, explained steps quickly today. Compare methods, track iterations, and download clean outputs for sharing with ease.
| Input | Digit sums (steps) | Final single digit | Iterations |
|---|---|---|---|
| 0 | 0 | 0 | 0 |
| 9 | 9 | 9 | 0 |
| 38 | 3+8=11 → 1+1=2 | 2 | 2 |
| 2026 | 2+0+2+6=10 → 1+0=1 | 1 | 2 |
| 987654 | 9+8+7+6+5+4=39 → 3+9=12 → 1+2=3 | 3 | 3 |
| ID-2026-001 | 2+0+2+6+0+0+1=11 → 1+1=2 | 2 | 2 |
The single digit sum is also called the digital root. For a non‑negative integer n, repeatedly sum its base‑10 digits until one digit remains.
The modulo‑9 property is why digit sums are used for quick checks: n mod 9 matches sumDigits(n) mod 9.
This calculator reduces any whole-number input to a single digit by repeatedly summing its decimal digits. The outcome is the digital root, and the number of repeat rounds is the additive persistence. For example, 2026 → 10 → 1 has digital root 1 and persistence 2.
In base 10, a non‑negative integer n maps to one of 0–9. When n = 0, the digital root is 0. When n > 0, the result falls in 1–9, so every positive input is classified into nine residue classes.
Iteration is transparent and easy to audit. Each pass computes S(n), the sum of digits. A 6‑digit value like 987654 produces 39 on the first pass, then 12, then 3, for a persistence of 3. Long inputs usually shrink rapidly because digit sums grow slowly compared with place value.
A fast method uses the identity dr(n) = 1 + ((n − 1) mod 9) for n > 0. This follows from 10 ≡ 1 (mod 9), meaning a number and its digit sum have the same remainder modulo 9. The calculator reports the modulo‑9 residue to support “casting out nines” checks.
For a string with k digits, both methods scan digits in O(k) time. The formula approach avoids repeated passes and is ideal for thousands of digits. A maximum-iteration cap provides safety for unusual inputs while still finishing typical workloads instantly.
Many datasets include separators such as spaces, commas, or identifiers like ID-2026-001. When “Ignore non-digits” is enabled, the calculator extracts digits only, then computes results on the cleaned number. This is useful for batch labels, invoice strings, and pasted columns from spreadsheets.
Digital roots support quick mental validation: if two values should match, their residues modulo 9 should also match. They are also used in check-digit teaching examples, classroom number theory demonstrations, and data sanity checks. Additive persistence can be tracked as a compact “digit complexity” indicator across records.
Export buttons generate CSV for spreadsheets and a lightweight PDF for documentation. Including the input, cleaned digits, method, persistence, and steps makes results reproducible. When sharing outputs, always state whether non-digit characters were ignored to keep comparisons consistent.
It is the final one-digit result obtained by repeatedly adding the digits of a non-negative integer until only one digit remains, also called the digital root.
Because in base 10, a number and its digit sum have the same remainder modulo 9. This makes digital roots a fast consistency check using “casting out nines”.
Yes, for non-negative integers in base 10 they match. The formula is a shortcut to the same endpoint that iterative summing reaches after multiple rounds.
It is the number of digit-sum rounds required to reach a single digit. For example, 38 needs two rounds: 3+8=11, then 1+1=2.
Yes. Enable “Ignore non-digits” to extract digits from formatted strings such as “1,234,567” or “ID-2026-001” before computing the result.
It processes the input as a digit string, so size is limited mainly by memory. The formula method is recommended for very long inputs because it needs only one scan.
Export the raw input, the cleaned digits used, the final single digit, additive persistence, method, and steps. This makes the calculation easy to reproduce and verify.
Use this tool to verify digits quickly and reliably.
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.