How to Calculate Cumulative

Cumulative Sum Formula:

\[ C_i = \sum_{j=1}^{i} x_j = x_1 + x_2 + \cdots + x_i \]

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Cumulative Sum?

The cumulative sum (also called running total or partial sum) is the sum of a sequence of numbers which is updated each time a new number is added to the sequence, by adding the value of the new number to the previous running total.

2. How to Calculate Cumulative Values

The cumulative sum is calculated using the formula:

\[ C_i = \sum_{j=1}^{i} x_j = x_1 + x_2 + \cdots + x_i \]

Where:

\( C_i \) — Cumulative sum up to the i-th element
\( x_j \) — The j-th value in the sequence
\( i \) — The current position in the sequence

Example: For values [2, 4, 3, 5], the cumulative sum would be [2, 6, 9, 14].

3. Applications of Cumulative Sum

Details: Cumulative sums are used in various fields including finance (running balance), statistics (moving averages), computer science (prefix sums), and data analysis to track progress over time.

4. Using the Calculator

Tips: Enter your numerical values separated by commas (e.g., 5, 3, 8, 2). The calculator will compute and display the cumulative sum at each step.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between sum and cumulative sum?
A: A sum gives the total of all values, while cumulative sum shows the running total at each step of the sequence.

Q2: Can I calculate cumulative sum for negative numbers?
A: Yes, the calculator works with both positive and negative numbers, as well as decimal values.

Q3: What if I have non-numeric values in my input?
A: The calculator will ignore any non-numeric values and only process valid numbers.

Q4: How is cumulative sum used in real-world applications?
A: Common applications include tracking account balances, calculating running scores, monitoring cumulative sales, and analyzing time-series data.

Q5: Can I calculate cumulative products or other operations?
A: This calculator specifically calculates cumulative sums. Other cumulative operations (like products) would require different calculations.