Order of Operations (PEMDAS) Calculator

Order of Operations (PEMDAS) Calculator

There’s a kind of pause that happens when a math problem stares back with too many symbols. Parentheses stacked on parentheses. Numbers raised to strange little powers. A division sign waiting somewhere in the middle. Everything tangled into one expression. And in that moment, the question isn’t just what do I solve first? Sometimes it’s what if I don’t know how?

In math, there is a way through the knot. A pattern. A set of rules called the Order of Operations that tells us how to untangle even the most complicated expressions, one strand at a time. Not by guessing, but by following a path that mathematicians around the world agree on. A kind of grammar for numbers. Let’s begin with the rules.

Breaking Down PEMDAS

The rules that guide the order of operations are often remembered through the word PEMDAS. It’s not a perfect word. It doesn’t roll off the tongue or carry any natural poetry. But it works. It helps keep the steps in order.

Each letter stands for a different type of operation, and the sequence matters. Think of it less like a strict hierarchy and more like a set of gentle instructions—like steps in a recipe, or layers in a painting. If followed carefully, they reveal something clear beneath the mess.

Here’s what PEMDAS stands for:

• P – Parentheses
• E – Exponents
• M – Multiplication
• D – Division
• A – Addition
• S – Subtraction

Some versions use the phrase Please Excuse My Dear Aunt Sally. It’s silly. And honestly, it’s okay to forget the aunt, as long as the order stays intact.

Now, let’s slow down and look at each one.

Parentheses

Anything inside parentheses comes first. Always.

They act like containers. They hold a part of the problem that needs to be solved before anything else.

For example:

(3 + 2) × 4

First, solve what’s inside the parentheses. That gives you 5 × 4, which equals 20.

Without parentheses: 3 + 2 × 4

You would multiply first. 2 × 4 is 8, then add 3, which gives you 11. Same numbers, different result. That’s the power of grouping.

Exponents

After parentheses, look for exponents. These are the small numbers written just above and to the right of a base number. They show repeated multiplication.

2³ means 2 × 2 × 2, which equals 8.

Exponents often appear in expressions that feel unfamiliar at first. But they follow the same pattern every time. Solve them after parentheses, and before any multiplication or division.

Multiplication and Division

Multiplication and division are next. They belong on the same level. Work through them from left to right, depending on which one appears first in the expression.

For example:

16 ÷ 4 × 2

Start with 16 ÷ 4, which is 4. Then multiply by 2, to get 8.

Do not multiply before dividing just because M comes before D in the acronym. They share equal priority. Let the order in the expression guide you.

Addition and Subtraction

Finally, addition and subtraction. Like multiplication and division, they are equals. Work from left to right.

Take this example:

12 - 5 + 3

First, subtract 5 from 12. That gives 7. Then add 3, for a final result of 10.

Solving out of order changes everything. These last steps may look simple, but they still follow the same structure.

Holding the Pattern

So, the full order is: parentheses, exponents, multiplication, or division (from left to right), then addition or subtraction (also left to right).It is not about rushing through to get the answer. It is about building trust in a sequence. There is calm in knowing that each part has its place.

When the order is followed, even a complicated expression becomes something you can work with. Step by step, the path becomes clearer. There is no need to guess. There is no need to feel lost. The pattern holds.

Examples of Order of Operations

The best way to understand the order of operations is to watch it in motion. One step at a time. No shortcuts, no assumptions, just quiet clarity.

These examples follow the PEMDAS sequence: Parentheses, Exponents, Multiplication and Division (from left to right), then Addition and Subtraction (also from left to right). Each one begins with a full expression and walks through the process gently, showing what’s done, and why it matters.

Example 1

Expression:

3 + 6 × (4 + 2) ÷ 3

Step 1: Parentheses

Look for anything grouped.

(4 + 2) becomes 6

Now the expression is:

3 + 6 × 6 ÷ 3

Step 2: Multiplication and Division (left to right)

Start with 6 × 6 = 36

Then 36 ÷ 3 = 12

Now we have:

3 + 12

Step 3: Addition

3 + 12 = 15

Final Answer: 15

Why this matters:

Solving out of order—like adding 3 + 6 first—would change the path entirely. Instead of 15, the answer becomes something else. Every step builds on the one before it.

Example 2

Expression:

(8 - 3)² + 10 ÷ 2

Step 1: Parentheses

8 - 3 = 5

Now:

5² + 10 ÷ 2

Step 2: Exponents

5² = 25

Now:

25 + 10 ÷ 2

Step 3: Division

10 ÷ 2 = 5

Now:

25 + 5

Step 4: Addition

25 + 5 = 30

Final Answer: 30

Why this matters:

If the exponent had been forgotten, and someone had just added 5 + 10, the square would be lost entirely. Exponents carry weight, even when they look small.

Example 3

Expression:

16 ÷ 4 × 2 + 1

Step 1: Multiplication and Division (left to right)

First, 16 ÷ 4 = 4

Then 4 × 2 = 8

Now:

8 + 1

Step 2: Addition

8 + 1 = 9

Final Answer: 9

Why this matters:

If someone multiplied before dividing—choosing 4 × 2 = 8 first—then tried 16 ÷ 8, they’d get 2. That answer is neat, but it’s wrong. Neat doesn’t always mean right.

Example 4

Expression:

7 + 2 × (3 + 1)²

Step 1: Parentheses

3 + 1 = 4

Now:

7 + 2 × 4²

Step 2: Exponents

4² = 16

Now:

7 + 2 × 16

Step 3: Multiplication

2 × 16 = 32

Now:

7 + 32

Step 4: Addition

7 + 32 = 39

Final Answer: 39

Why this matters:

Skipping steps or doing them out of order might seem faster, but it leads to confusion. In expressions like this, even one small shortcut can change the entire answer.

Mistakes People Make (And Why They Matter in Real Life)

Mistakes are natural. Everyone makes them, especially when a problem feels crowded or rushed. But the point isn’t to avoid mistakes entirely. The point is to notice them, understand them, and see how they change more than just a number.

Because math doesn’t stay on the page. It spills into cooking measurements, paychecks, building plans, shared bills. A single step in the wrong order can shift the outcome—and sometimes, that shift means more than just a different answer. It means a different reality.

Let’s look at some common mistakes, and how they play out beyond the classroom.

Mistake 1: Thinking Multiplication Always Comes Before Division

PEMDAS puts M before D, so many people assume multiplication should come first. But that’s not how the pattern works. Multiplication and division are equals. What matters is the order they appear, from left to right.

Example:

24 ÷ 6 × 2

The correct path: 24 ÷ 6 = 4, then 4 × 2 = 8

If someone multiplies first: 6 × 2 = 12, then 24 ÷ 12 = 2

Why it matters:

Imagine someone is doubling a recipe that calls for 24 ounces of flour to make 6 loaves. If they do the steps out of order, they might only use 2 ounces per loaf instead of 4. That’s the difference between a hearty slice of bread and something flat and underbaked.

In money? That kind of error can mean budgeting half of what’s needed. Or miscalculating time and falling behind schedule. It adds up fast.

Mistake 2: Solving Left to Right Without Noticing Parentheses or Exponents

Left to right is part of the rule. But it only applies after you’ve taken care of grouping and powers. Skipping those steps creates a false sense of progress.

Example:

5 + (2 × 3)²

The correct path: 2 × 3 = 6, then 6² = 36, then add 5 to get 41

The mistake path: 5 + 2 = 7, then 7 × 3 = 21, then square that? It becomes a mess

Why it matters:

In architecture, for example, an area might be calculated using exponents. Getting that wrong could throw off material costs. In programming, an incorrect order might crash a function or return a broken result. These aren’t just math errors. They’re structural ones.

Mistake 3: Skipping Parentheses Entirely (or Misreading Them)

Parentheses are not optional. They are instructions. Ignoring them leads to a completely different expression, and a completely different result.

Example:

4 + 2 × 5 = 14

(4 + 2) × 5 = 30

Why it matters:

Think about splitting a dinner bill. If the total includes tax and tip grouped together, and someone ignores the grouping, they might divide incorrectly. One person ends up paying more, another pays less. It creates tension.

Or think about adjusting ingredients in a recipe that serves multiple people. Getting the grouping wrong could mean too much salt, too little sugar, not enough servings. It changes the outcome in small but tangible ways.

How to Use the Symbolab Order of Operations (PEMDAS) Calculator

Sometimes it helps to have a second set of eyes. Or a calm voice walking you through the steps, just to be sure the path you're taking is the right one.

The Symbolab Order of Operations Calculator is a tool designed to do just that. It doesn’t just give you the final answer. It shows the work. It explains the steps. It helps you see the pattern, not just memorize it. Here’s how to use it.

Step 1: Enter the Expression

There are three ways to input your problem:

• Type it using a regular keyboard. This works well for straightforward problems like 3 + 6 × (4 + 2) ÷ 3
• Use the built-in math keyboard, especially helpful for expressions with exponents, square roots, fractions, or absolute value bars. It gives you the symbols you might not find on your own keyboard.
• Scan a handwritten expression using your device’s camera. If you're working from paper and don’t feel like retyping it, this is a good shortcut. The app will read your writing and convert it into a solvable expression.

Try typing this into the calculator:

3 + 6 × (4 + 2) ÷ 3

Watch how it reacts. Notice the steps it shows.

Step 2: Click “Go”

Once your expression is entered, click the “Go” button. There’s no need to review or double-check right away. The calculator will catch any formatting issues and offer suggestions if something seems off.

This step is simple. It’s the moment you move from wondering to watching.

Step 3: View the Step-by-Step Breakdown

This is where the tool shines.

Instead of jumping to the final answer, the calculator walks through each operation in the correct order.

It shows:

• What part was solved first
• Why that step came next
• How the expression changed after each operation

There’s also an option to go one step at a time, if you want to slow it down. Each step includes a short explanation. You can follow along, line by line, like tracing the work of someone thinking aloud.

And if something still feels confusing? There’s a built-in chat with Symbo feature. You can ask questions and get guidance in real time. It’s not just about getting the answer—it’s about making sense of the path.

Learning, Not Just Solving

The Symbolab calculator isn’t there to replace your thinking. It’s there to support it. To catch the steps you missed. To confirm the ones you got right. And maybe, most importantly, to remind you that working through something carefully is not a weakness. It’s a strength.

Use it when you're stuck. Use it when you're unsure. Use it even when you think you’ve got it, just to double-check. Because sometimes learning looks like solving. And sometimes it just looks like slowing down and paying attention.