Digital Root Calculator API: Compute Repeated Digit Sums

The digital root is the single-digit value obtained by repeatedly summing a number's digits until only one digit remains. The Digital Root API calculates this value along with the intermediate steps, useful for checksums, numerology, and mathematical analysis.

What is Digital Root?

The digital root (also called repeated digital sum) is calculated by summing all digits of a number, then summing the digits of the result, and repeating until a single digit (1-9) remains. For zero, the digital root is 0.

Example: 9875

• Step 1: 9 + 8 + 7 + 5 = 29
• Step 2: 2 + 9 = 11
• Step 3: 1 + 1 = 2
• Digital root of 9875 is 2

Calculation Methods

There are two ways to find digital roots:

Iterative Method

Repeatedly sum digits until reaching a single digit. Shows each step.

Direct Formula

For n > 0: digital_root(n) = 1 + ((n - 1) mod 9)

This formula gives the answer instantly without iteration.

Mathematical Properties

• Digital root is always 1-9 (or 0 for input 0)
• Equivalent to n mod 9, except 0 maps to 9
• Used in divisibility tests (digital root 9 = divisible by 9)

Using the Digital Root API

TinyFn provides a simple endpoint for digital root calculation:

GET https://api.tinyfn.io/v1/math/digital-root?number=9875
Headers: X-API-Key: your-api-key

{
  "number": 9875,
  "digital_root": 2,
  "iterations": 3,
  "steps": [
    {"sum": 29, "digits": [9, 8, 7, 5]},
    {"sum": 11, "digits": [2, 9]},
    {"sum": 2, "digits": [1, 1]}
  ],
  "digit_sum": 29,
  "additive_persistence": 3
}

Parameters

Code Examples

JavaScript / Node.js

const response = await fetch(
  'https://api.tinyfn.io/v1/math/digital-root?number=12345',
  { headers: { 'X-API-Key': 'your-api-key' } }
);
const data = await response.json();
console.log(`Digital root of 12345: ${data.digital_root}`);
console.log(`Iterations required: ${data.iterations}`);

Python

import requests

response = requests.get(
    'https://api.tinyfn.io/v1/math/digital-root',
    headers={'X-API-Key': 'your-api-key'},
    params={'number': 999999999}
)
data = response.json()
print(f"Digital root: {data['digital_root']}")
print(f"Additive persistence: {data['additive_persistence']}")

cURL

curl "https://api.tinyfn.io/v1/math/digital-root?number=9875" \
  -H "X-API-Key: your-api-key"

Common Use Cases

• Checksum Validation: Verify data integrity using digit sums
• Numerology Apps: Calculate life path numbers and similar
• Divisibility Tests: Quick check for divisibility by 3 or 9
• Educational Tools: Teach digit manipulation and patterns
• Data Verification: Simple error detection in numeric data

Best Practices

1. Use direct formula: For just the result, the formula is faster
2. Show steps when teaching: Iteration steps help understanding
3. Know the properties: Digital root relates to modulo 9 arithmetic
4. Handle zero: Digital root of 0 is 0, not 9
5. Consider persistence: Number of iterations (additive persistence) is also interesting