Sum of Consecutive Integers Calculator

The Sum of Consecutive Integers Calculator is a powerful tool designed to quickly calculate the sum of sequential whole numbers. Whether you’re dealing with consecutive integers, consecutive odd integers, or consecutive even integers, this calculator simplifies the process by providing accurate results instantly.

Of course, if you want to find consecutive integers based on the sum, you can use our consecutive integers calculator.

Consecutive integers are simply whole numbers that follow each other in sequence. For instance, 1, 2, 3, 4, 5 are consecutive integers. 55, 56, 57, 58, 59, 60 are also consecutive integers. But 21, 22, 24, 25, 26 are not consecutive integers because 22 and 24 are not consecutive.

Consecutive Odd Integers: These are sequences of odd numbers, such as 1, 3, 5, 7, etc.

Consecutive Even Integers: These are sequences of even numbers, such as 2, 4, 6, 8, etc.

Before we start discussing the formula, let’s take a look at an example. What is the sum of 1 to 100? Is this example a bit familiar? Yes, a common math problem. How do you calculate it? Step by step, counting one number plus one number, or looking for another method?

I think there are only a few people who do the calculations step by step, so what should we do? That’s right, find a regular pattern! What regular pattern? The first number plus the last number is equal to 101, the second number add the penultimate number is equal to 101. The third number and the third penultimate number sum is 101. According to this rule, the sum of the 50th number and the penultimate 50 number is 101.

So the sum of 1 to 100 integers can be divided into 50 groups, and each group sum is 101, that is, 50*101=5050. The picture display below can be seen more clearly.

In further detail, 50 groups are equal to the total number 100 divided by 2. So the sum of 1 to 100 is equal to 100*(1+100)/2. Therefore, from this to the other, replace the starting number 1 with A, replace the ending number 100 with B, and total numbers from A to B is denoted by N.  Thus, the sum of consecutive integers from A to B formula is:

Well, the formula of summing consecutive numbers from A to B comes out: total numbers multiply by the sum of the first number and last number, then divide by 2.

For example, the sum of 100 to 300 integers.

Sum(100, 300) = 201 * (100+300) / 2 = 40200

Note: 201 means the number of all integers between 100 and 300.

Isn’t it simple, then look down.

If we do not need all the consecutive numbers, only need the sum of even numbers, how to calculate it?  First of all, we must know what is an even number? An even number is an integer that can be divisible by 2. Therefore, to calculate the sum of consecutive even numbers, we must find out all the even numbers first.

Still taking 1 to 100 as an example, according to the definition of even numbers, it can be easily concluded that there are 50 even numbers between 1 and 100. The first even number is 2, and the last even number is 100. According to the above formula of summing consecutive numbers, the sum of even numbers from 1 to 100 is:

SumEven(1,100) = 50 * (2+100) / 2 = 2550

50 means there are 50 even numbers between 1 and 100.

Like even numbers, odd numbers are integers that cannot be divisible by 2. There are also 50 odd numbers between 1 and 100. The first odd number is 1, and the last odd number is 99. So the sum of odd numbers between 1 and 100 is:

SumOdd(1,100) = 50 * (1+99) / 2 = 2500

After knowing the formula for summing continuous integers, you can calculate it by hand or use our calculator. Of course, it is more convenient to use our tool. Here are the steps to use.

1. Enter the starting number.
2. Enter the ending number.
3. Selection type, the default is consecutive integers, of course, you can choose even or odd numbers according to your needs.
4. Click the “Calculate” button.

1. Enter the starting number.
2. Enter the number of consecutive integers.
3. Selection type: the default is consecutive integers, of course, you can choose even or odd numbers according to your needs.
4. Click the “Calculate” button.

The tool is very convenient to use, you can try it yourself.

To deepen understanding, let’s give a few examples:

Example 1: Sum of 1 to 200 integers

Enter 1 in the first input box, enter 200 in the second input box, then click calculate button.

Example 2: Sum of even numbers from 1 to 200

Enter 1 in the first input box, enter 200 in the second input box, then select the even number type, and finally click calculate button.

Example 3: Sum of odd numbers from 1 to 200

Similar to the above, but select the odd integers type.

Example 4: Sum of 100 consecutive integers starting from 500

Enter the starting number 500 in the first input box, and enter the integer number 100 in the second input box, then click calculate button.

Example 5: Sum of 100 consecutive even numbers starting from 500

Put the starting number 500 in the first input box and the consecutive even number 100 in the second input box, then select the even number type, finally click calculate button.

Example 6: Sum of 100 consecutive even numbers starting from 500

The same as example 5, but select the odd type.

At this point, you should understand the mission of our calculator, here are some common problems: