Count (n): "+nums.length+"
Mean: "+(result/nums.length).toFixed(4);}}else if(type==='series'){var n=parseFloat(document.getElementById('countN').value);var a=parseFloat(document.getElementById('startA').value);var d=parseFloat(document.getElementById('diffD').value);if(isNaN(n)||isNaN(a)||isNaN(d)){alert('Please fill all arithmetic series fields');return;}result=(n/2)*(2*a+(n-1)*d);if(showSteps){details="Formula: Sₙ = n/2 * [2a + (n-1)d]
Calculation: "+n+"/2 * [2("+a+") + ("+n+"-1)"+d+"]
Calculation: "+(n/2)+" * ["+(2*a)+" + "+((n-1)*d)+"]";}}else if(type==='integers'){var n=parseFloat(document.getElementById('countN').value);var a=parseFloat(document.getElementById('startA').value);if(isNaN(n)||isNaN(a)){alert('Please enter N and starting point');return;}result=(n*(n+1)/2)-((a-1)*a/2);if(showSteps){details="Formula: Σk = [n(n+1)/2] – [(a-1)a/2]
Range: "+a+" to "+n+"
Calculation: "+(n*(n+1)/2)+" – "+((a-1)*a/2);}}document.getElementById('resultValue').innerHTML=result.toLocaleString();if(showSteps&&details!==""){document.getElementById('detailBox').innerHTML=details;document.getElementById('detailBox').style.display='block';}else{document.getElementById('detailBox').style.display='none';}}
How to Use the Sum Calculator
The Sum Calculator is a versatile tool designed to help you find the total of a list of numbers or calculate the sum of specific mathematical sequences. Whether you are adding up expenses, calculating an arithmetic progression, or finding the sum of the first N integers, this tool provides instant and accurate results.
To use the calculator, simply select the type of calculation you need from the dropdown menu:
- Sum of a List (Dataset)
- Choose this for a raw list of numbers. You can paste data from spreadsheets or documents separated by commas, spaces, or new lines.
- Arithmetic Series
- Use this for sequences with a constant difference. You will need the number of terms (n), the starting value (a₁), and the common difference (d).
- Sum of First N Integers
- Quickly find the sum of all whole numbers from a starting point up to N (e.g., the sum of all numbers from 1 to 100).
Summation Formulas and Logic
Summation is a fundamental concept in mathematics, often represented by the Greek letter Sigma (Σ). The formulas used by our sum calculator depend on the input method chosen:
1. Standard Summation
For a dataset $x_1, x_2, …, x_n$, the formula is simply the addition of all values:
Total = x₁ + x₂ + x₃ + … + xₙ
2. Arithmetic Series Formula
An arithmetic series is the sum of terms in a sequence where the difference between consecutive terms is constant. The formula is:
Sₙ = (n/2) * [2a₁ + (n – 1)d]
- n: The number of terms to be added.
- a₁: The first term in the sequence.
- d: The common difference between terms.
Sum Calculator Examples
Example 1: Dataset Sum
You have five invoices with the following amounts: $120.50, $45.00, $300.25, $15.75, and $88.00.
- Select "Sum of a List"
- Enter: 120.5, 45, 300.25, 15.75, 88
- Click Calculate.
- Result: 569.50
Example 2: Sum of Numbers from 1 to 100
To find the sum of all integers from 1 to 100 using the integer range mode:
- Select "Sum of First N Integers"
- Enter First Term (a₁): 1
- Enter Number of Terms (n): 100
- Formula applied: (100 * 101) / 2
- Result: 5,050
Frequently Asked Questions
Can this calculator handle negative numbers?
Yes. In the "List" mode, you can enter negative values (e.g., -10, 50, -5). The sum calculator will treat them as subtractions from the total.
What is the difference between a sum and a mean?
The sum is the total value of all numbers added together. The mean (average) is that sum divided by the number of values in the set. If you check "Show Summation Details," this calculator will provide both the total and the mean.
How many numbers can I enter in the list?
There is virtually no limit for standard use. You can paste thousands of numbers from a column in Excel or a text file, and the calculator will process them instantly.