Consecutive Integers Calculator

Work out consecutive integers instantly with clear inputs, formula shown and shareable results.

About Consecutive Integers Calculator

A run of k consecutive integers starting at a sums to ka + k(k−1)/2. Solving for a gives a = (S − k(k−1)/2) / k, which is a whole number only for certain combinations of S and k.

Formula

Sum of a run

S = k·a + k(k − 1)/2 ⇒ a = (S − k(k−1)/2) / k

Worked example

With the default values below, Consecutive Integers Calculator returns First integer of 9.000000. Change any input above and every figure here is recalculated in your browser.

Inputs used

Required sum: 100
How many consecutive integersaccepts 1–1,000: 8

Results

First integer: 9.000000
Last integer: 16.000000
The run: 9, 10, 11, 12, 13, 14, 15, 16
Sum of the run: 100.000000

Step by step

1Values used
2Sum of a run
3First integer= 9.000000
4Last integer= 16.000000
5The run= 9, 10, 11, 12, 13, 14, 15, 16
6Sum of the run= 100.000000

Assumptions and limits

The result is derived only from the 2 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 6 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

Which 8 consecutive integers sum to 100?

a = (100 − 28)/8 = 9, so 9 through 16.

Why does it sometimes fail?

For an even count k the sum must be k/2 times an odd number; otherwise no whole-number run exists.