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Math Calculators

Sum of Natural Numbers Calculator

Verified formula Updated Jun 2026 Private — runs on your device

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Verified formula Private

Sum of 1 to n

5,050

For general information only — not financial, tax, legal or medical advice. Verify before you rely on it.

How to use the Sum of Natural Numbers Calculator

The Sum of Natural Numbers Calculator works out your sum of 1 to n in an instant. Enter up to number (n) and the result updates as you type — it is free, needs no sign-up, and runs entirely in your browser so your figures stay private.

  1. Enter the up to number (n).
  2. Read off your sum of 1 to n — the calculator updates automatically, with no button to press.

Formula

The Sum of Natural Numbers Calculator uses the formula:

Sum of 1 to n = Up to number (n) × (Up to number (n) + 1) ÷ 2

Worked example

For example, with up to number (n) of 100, the sum of 1 to n is 5,050.

Inputs used
Up to number (n) 100
Results
Sum of 1 to n 5,050

Results are estimates for educational use, not professional advice.

Frequently asked questions

Use the formula n × (n + 1) ÷ 2. The sum of 1 to 100 is 100 × 101 ÷ 2 = 5050.

Pairing the first and last numbers, second and second-last, and so on, gives n ÷ 2 pairs each summing to (n + 1).

The trick is famously linked to the mathematician Gauss, who is said to have used it as a schoolboy to add 1 to 100 quickly.

Each sum from 1 to n is a triangular number, since that many dots form a triangle. The 100th triangular number is 5050.

Enter the up to number (n). Read off your sum of 1 to n — the calculator updates automatically, with no button to press.

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