How it works
A triangular arrangement has rows containing 1, 2, 3 and so on up to n objects. Five rows contain 1 + 2 + 3 + 4 + 5 = 15 objects. At n = 0 the empty sum is zero. This is a sum of consecutive integers, not a sum of arbitrary list entries.
Inputs and units
| Input | Example value | What to enter |
|---|---|---|
| Final integer n | 10 | Enter a numeric value. Use a whole number. Use a non-negative value. |
Worked example
Show example inputs and results
This example is generated by the same calculation engine using the starting values in the form. Your own inputs produce your own result.
- Final integer n
- 10
Complete example results
- Triangular number
- 55
Reading the result
Use quantities on the same basis. The starting value in percentage change, the denominator in a ratio and the length unit in geometry determine the meaning of the answer. Check the formula conditions alongside the example.
Questions and answers
Can I use the example values for my own calculation?
The example values illustrate the calculation. Replace every input with your own information, especially dates, rates and the selected operation.
Does n mean the number of pairs in a group?
Here n counts rows, or the last added integer. The number of distinct pairs from n people is n(n − 1)/2 instead and belongs to a combinations calculation.
Why are some results rounded?
Results display up to 8 decimal places. Calculations use the unrounded values; very small values use scientific notation. JavaScript floating-point arithmetic can introduce tiny rounding differences.
Are my inputs sent to a server?
The calculator processes inputs in your browser. Its code does not send your values to a server.