Integer Calculator

What this calculator does

So, you have two numbers and you want to combine them, and you want a choice of how. This tool is a compact calculator that takes two values, a and b, and applies whichever of seven operations you pick from a dropdown. Despite the name, it is happy with decimals as well as whole numbers, and it covers far more than plain integer arithmetic.

Pick an operation, enter the two numbers, and the result comes back rounded to two decimal places.

How to use it

1. Choose an operation from the dropdown.
2. Enter the two numbers, a and b.
3. Press Calculate.

The seven operations

The dropdown offers seven ways to combine your two numbers. Four are the familiar arithmetic operations: addition, subtraction, multiplication, and division. The other three go further: raising a to the power b, taking the b root of a, and finding the logarithm of b to the base a. So the tool is really a small all-in-one calculator, stretching from the arithmetic everyone knows into the exponent, root, and logarithm operations that usually need their own buttons. Whichever you select, the tool shows the matching expression and works out the value.

The four basic operations

The first four choices are the bedrock of arithmetic. Addition gives a plus b, the total of the two. Subtraction gives a minus b, the difference. Multiplication gives a times b, the result of adding a to itself b times. Division gives a divided by b, how many times b fits into a, expressed as a decimal here rather than a quotient and remainder. These four are the operations you use every day, and having them alongside the more advanced ones means one tool can carry a whole calculation from start to finish.

Power, root, and logarithm

The last three operations are the ones that give this calculator its reach. The exponent option raises a to the power b, multiplying a by itself b times. The root option finds the b root of a, which is the reverse of raising to a power: it asks what number, multiplied by itself b times, gives a. The logarithm option finds the logarithm of b to the base a, which asks what power you must raise a to in order to reach b. These three are tightly linked, powers, roots, and logarithms are three views of the same relationship, and this tool puts all of them a single dropdown apart.

A worked example

Take a as 12 and b as 4. Addition gives 16, subtraction gives 8, multiplication gives 48, and division gives 3. Switch to the exponent option and 12 to the power 4 is 20736. The root option gives the fourth root of 12, roughly 1.86, and the logarithm option gives the logarithm of 4 to base 12, roughly 0.56. One pair of numbers, seven different answers depending on the operation you choose.

When you want just one operation

This tool is handy when you want several operations in one place, but sometimes you want a calculator built around a single one, with its own explanation and options. For raising a number to a power, the exponent calculator focuses on just that. For roots, the root calculator handles any degree of root on its own. And for logarithms, the logarithm calculator lets you work with a chosen base directly. Reach for those when one operation is the whole job, and this one when you want the full set together.

Questions people ask

What can this calculator do?

It combines two numbers using any of seven operations: addition, subtraction, multiplication, division, exponent, root, and logarithm.

Does it only work with integers?

No. Despite the name it accepts decimals too, and the advanced operations often return decimal results, shown to two decimal places.

What does the root option do?

It finds the b root of a: the number that, multiplied by itself b times, gives a. It is the reverse of raising to a power.

What does the logarithm option do?

It finds the logarithm of b to the base a: the power you must raise a to in order to reach b.

Is there a tool for just one operation?

Yes. The exponent, root, and logarithm calculators each focus on a single operation with their own options.

References

On arithmetic operations. Arithmetic covers addition, subtraction, multiplication, division, and the related operations of powers, roots, and logarithms.

1. Lynda Sherman and Eric W. Weisstein, "Arithmetic," from MathWorld, a Wolfram resource, on the operations of numerical computation.
2. Eric W. Weisstein, "Logarithm," from MathWorld, a Wolfram resource, on the logarithm operation included in this calculator.