Type 2 + 3 × 4 on a Basic and a Scientific Calculator and You'll Get Two Different Answers

By Aliyah Jenkins · Updated September 30, 2026 · 8 min read

Grab the cheap calculator from your desk drawer and type 2 + 3 × 4 =. Now type exactly the same keys into a scientific calculator or the calculator app on your phone. Same buttons, same order, and yet the two screens disagree.

Neither calculator is broken. They're following two different sets of rules about when to do the math, and once you understand the difference, you'll never trust a calculator blindly again.

01What Each Calculator Is Actually Doing

The difference comes down to one question: does the calculator do the math as you go, or does it wait until it has seen the whole problem?

Most basic four-function calculators work as you go. This method is called immediate execution, or chain calculation. Every time you press an operator key like + or ×, the calculator finishes the previous step and shows you a running total. Here's what that looks like, keypress by keypress:

Look at the fourth step. The moment you press ×, the basic calculator adds 2 and 3 without knowing a multiplication is coming. By the time you type the 4, the addition is already locked in.

A scientific calculator waits. When you press ×, it notices that multiplication should happen before the addition, so it holds onto the 2 and the + and deals with 3 × 4 first. Only when you press = does it finish the job: 3 × 4 = 12, then 2 + 12 = 14.

02So Which Answer Is Correct?

Written as a math problem, 2 + 3 × 4 equals 14. That's what any math teacher, textbook, spreadsheet, or programming language will tell you, because of the convention known as the order of operations.

The rule says to work through a problem in this order: anything in brackets first, then exponents (powers and roots), then multiplication and division from left to right, and finally addition and subtraction from left to right. Different countries teach it with different memory aids:

All four describe the same idea. Multiplication beats addition, so the 3 × 4 happens before the 2 is added.

03Why Math Has an Order of Operations at All

The order of operations isn't a law of nature. It's an agreement, like driving on one side of the road, that lets everyone read the same expression the same way.

Without it, every expression would need a thicket of brackets to avoid confusion. Mathematician Hung-Hsi Wu of the University of California, Berkeley, has explained that the convention exists mainly to save writing. Algebra is full of expressions like 3x² + 2x + 5, and the order of operations lets you write them cleanly instead of as ((3 × (x²)) + (2 × x)) + 5.

There's also a practical logic to multiplication ranking higher. If a shop sells 3 notebooks at ₱40 each plus a ₱10 pen, you naturally calculate 10 + 3 × 40 as ten plus the cost of the notebooks: ₱130. The multiplication describes a group of things that belong together, so it gets bundled up first.

04Why Basic Calculators Ignore the Rule

If 14 is correct, why do millions of basic calculators give 20? Because they were built for a different job.

Basic calculators descend from mechanical adding machines, the clunky office devices accountants and shopkeepers used to total up columns of figures. Those machines kept a running total, and so do basic calculators. If you're adding up a stack of receipts, a running total is exactly what you want: you can see the subtotal after every entry and catch mistakes as you go.

There were engineering reasons too. Early pocket calculators had tiny amounts of memory and simple seven-segment displays that could only show numbers, not a whole written expression. Doing each step immediately meant the calculator only ever had to remember one number and one pending operation. Holding a full expression in memory and sorting out priorities required more complex, more expensive chips.

According to the overview of calculator input methods on Wikipedia, this chain-calculation style is still used on most simple four-function calculators, and even the Standard mode of the Windows calculator works this way, while its Scientific mode follows the order of operations.

05How a Scientific Calculator Holds Its Thoughts

To follow the order of operations, a calculator needs to remember unfinished steps. When you type 2 + 3 ×, the scientific calculator stores the 2 and the pending addition in a kind of waiting list, then works on the higher-priority multiplication before returning to finish the addition.

Manufacturers have given their systems different names. Texas Instruments called an early version the Algebraic Operating System (AOS) and a later one the Equation Operating System (EOS), and it publishes a short explanation of the difference. Casio uses the name V.P.A.M. (Visually Perfect Algebraic Method), and Sharp calls its approach D.A.L. (Direct Algebraic Logic). Modern scientific and graphing calculators also show the whole expression on screen, so you can check it before pressing =.

Some calculators took a completely different path. Hewlett-Packard became famous in the 1970s for Reverse Polish Notation, where you enter the numbers first and the operation after. On those calculators, 2 + 3 × 4 is typed as 3, Enter, 4, ×, 2, +. It sounds strange, but it needs no brackets at all, and many engineers still swear by it.

06How to Get 14 on a Basic Calculator

You don't need a new calculator. You just need to feed the problem in an order that matches how the machine thinks.

07Other Calculator Traps Worth Knowing

The negative number trap

Computer scientist Harold Thimbleby has pointed out that 4 × (−5) can give three different answers on a basic calculator, depending on which keys you press. Press × then − then 5, and many calculators treat the minus as a correction, replacing × and calculating 4 − 5 = −1. Press the ± key before the 5, and some calculators ignore it, giving 20. You usually have to press ± after the 5 to get the correct −20.

The viral puzzle problem

Social media regularly explodes over puzzles like 6 ÷ 2(1 + 2). The debate comes from the implied multiplication in "2(1 + 2)," written without a × sign. Some people, and some calculators, treat that as a single bundled unit, giving 1. Others follow a strict left-to-right reading, giving 9. Different calculator brands, and sometimes different models from the same brand, have handled it differently. The real lesson is that the problem is badly written, and a pair of extra brackets would end the argument.

The spreadsheet surprise

Spreadsheets follow the order of operations, so =2+3*4 in Excel gives 14. But Excel has a quirk of its own: it applies a leading minus sign before exponents, so =-2^2 returns 4, while most math teachers would say −4.

08Test Every Calculator You Own

This is a fun two-minute experiment for your desk, your family, or your classroom. Type 2 + 3 × 4 = into every calculator you can find and compare the results. Here's what you'll typically see, though individual models can vary:

If you find a calculator that surprises you, it's a great conversation starter, and a useful reminder to double-check any important calculation, especially on a device you don't know well.

09Frequently Asked Questions

10Sources and Further Reading

1. Wikipedia. Calculator input methods.
2. Texas Instruments. Differences Between Algebraic Operating System (AOS) and Equation Operating System (EOS).
3. Wu, H. "Order of operations" and other oddities in school mathematics. Department of Mathematics, University of California, Berkeley.
4. Thimbleby, H. (1998). A new calculator and why it is necessary. Middlesex University.