Sum Calculator

Instantly add numbers and find the total, count, and average. Supports commas, spaces, and new line inputs.

Enter Numbers

Sum (Total)

Count

Average

Ignored

About the Sum Calculator

The Sum Calculator instantly adds any list of numbers and returns the total, along with the count, average, and number of ignored inputs. It's ideal for quickly totaling budgets, scores, measurements, or any list of values without needing a spreadsheet. To find the arithmetic mean of your data, use the Average Calculator.

Formula

Sum = a₁ + a₂ + a₃ + ... + aₙ

In sigma notation: Σaᵢ (for i = 1 to n)

Example Calculations

Budget totals: 1200 + 850 + 320 + 75 = 2,445
Test scores: 88 + 92 + 76 + 95 + 84 = 435
With negatives: 50 + (−30) + 20 = 40

Common Real-World Uses

Budgeting — add up monthly expenses or income sources
Inventory — total unit counts across multiple product categories
Grading — sum of points earned before calculating a final grade percentage
Data analysis — quickly total a column of exported spreadsheet values
Payroll — sum of hours worked across a pay period

Sum of Consecutive Integers (Gauss Formula)

For consecutive integers from 1 to n, there's a well-known shortcut formula:

Sum (1 to n) = n × (n + 1) ÷ 2

Example: Sum of 1 to 100 = 100 × 101 ÷ 2 = 5,050

Sum vs. Product

Sum (Σ) uses addition; product (Π) uses multiplication. The sum of 2, 3, and 4 is 2 + 3 + 4 = 9. The product is 2 × 3 × 4 = 24. This calculator computes sums only.

Accepted Input Formats

Comma-separated: 5, 10, 15, 20
Space-separated: 5 10 15 20
Line-separated: one number per line
Negative numbers and decimals fully supported

Frequently Asked Questions

How do you calculate the sum of numbers?

Add all the numbers together. For example, 5 + 10 + 15 + 20 = 50. The Sum Calculator does this instantly for any list you provide, no matter the size.

What is the sum of 1 to 100?

The sum of all integers from 1 to 100 is 5,050. This follows the Gauss formula: n × (n + 1) ÷ 2 = 100 × 101 ÷ 2 = 5,050.

What is the difference between sum and product?

Sum is the result of adding numbers (e.g., 2 + 3 + 4 = 9). Product is the result of multiplying them (e.g., 2 × 3 × 4 = 24). This calculator computes sums only.

What does Σ (sigma) mean in math?

Σ (uppercase sigma) is the mathematical symbol for summation — it means 'add up all values in this series.' For example, Σ(i=1 to 4) i means 1 + 2 + 3 + 4 = 10.

Can I enter negative or decimal numbers?

Yes. The Sum Calculator fully supports negative values (e.g., -4.5) and decimals (e.g., 7.25). They are included in the total just like any other number.

What input formats does the Sum Calculator accept?

Numbers can be separated by commas, spaces, or line breaks — for example '5, 10, 15' or one number per line. Mixed formats in the same input are handled automatically.

What additional results does the calculator show?

In addition to the total sum, it shows the count of valid numbers, the arithmetic average, and how many invalid inputs were ignored.

Is there a difference between sum and total?

In everyday contexts, 'sum' and 'total' mean the same thing — the result of adding all numbers together. In formal mathematics, 'sum' specifically refers to addition, while 'total' is more general.