The first calculators
Tell the story of mechanical calculators before digital devices.
Quick answer
The first calculators were mechanical devices that could add and subtract numbers by hand, like the abacus, Pascaline, and Leibniz wheel. They were used by merchants, scientists, and mathematicians long before computers existed.
Learning outcome
By the end of this page, you will understand how people calculated before computers and how these early machines helped with maths in daily life.
- You can name three early mechanical calculators
- You can explain how one of these machines worked
- You can show how these machines helped people in real life
- You can imagine using one of these machines
Why this matters
Understanding how people calculated before computers helps us appreciate the amazing progress in maths and technology. It also shows how clever humans were at solving problems with simple tools. You might even find yourself using some of the same thinking when you play games or solve puzzles!
How it works
Before calculators, people used different tools to do maths:
- Abacus – A frame with beads that move to show numbers
- Pascaline – A machine that could add and subtract using wheels
- Leibniz Wheel – A more advanced machine that could multiply and divide
Each machine had its own way of moving parts to make maths easier.
Examples you can see
Let's look at how these early machines worked:
The Abacus
The abacus is one of the oldest calculators. It looks like this:
| Row | Number of Beads | What it shows |
|---|---|---|
| Top row | 2 | Each bead = 5 |
| Bottom row | 5 | Each bead = 1 |
For example, if you want to show 7, you move one bead from the top row (5) and two beads from the bottom row (2). That makes 7.
The Pascaline
Blaise Pascal made a machine in 1642 that could add numbers. It had wheels with numbers on them:
- Each wheel shows a digit (0 to 9)
- When you turn a wheel, it adds one number
- To add 23 + 45, you turn the wheels to show 23, then turn them again to add 45
The Leibniz Wheel
Gotfried Wilhelm Leibniz made a better machine in 1673 that could multiply and divide:
- It used a wheel with teeth to do multiplication
- You turned a crank to make it work
- It was more complex but could do harder maths
Try it as a mini adventure
Imagine you are a merchant in the 1600s who needs to calculate how much money you have after selling goods. You have a Pascaline machine with you. You sell:
- 3 apples for 2 coins each
- 5 oranges for 3 coins each
- 2 bananas for 1 coin each
How much money do you earn?
Step 1: Calculate each fruit’s cost
- Apples: 3 × 2 = 6 coins
- Oranges: 5 × 3 = 15 coins
- Bananas: 2 × 1 = 2 coins
Step 2: Add all the coins
- 6 + 15 + 2 = 23 coins
Step 3: Use your Pascaline to show 23 coins
- Turn the wheels to show 23
You now have 23 coins to spend on more fruit!
Common mistakes
- Mistake: Thinking all early calculators could multiply and divide.
- Why it happens: Some people mix up the Pascaline and Leibniz Wheel.
- Fix: Remember: Pascaline only added and subtracted. Leibniz Wheel could multiply and divide.
- Mistake: Confusing the abacus with a modern calculator.
- Why it happens: Both help with maths, but the abacus is a physical tool.
- Fix: The abacus uses beads, not buttons or screens.
- Mistake: Thinking these machines were hard to use.
- Why it happens: People forget that early machines were designed to be simple.
- Fix: These machines were made to make maths easier, not harder.
Parent and carer guide
Help your child understand these early machines by:
- Showing them a simple abacus or drawing one on paper
- Playing a pretend game where they use a Pascaline to add numbers
- Reading a short story about a merchant using a calculator
- Encouraging them to build a simple machine with blocks or toys
- Asking questions like, "How would you show 10 on the abacus?"
Remember: These machines are not just history. They show how maths has always been about solving problems. Let your child see the connection between old tools and modern ones.
Practice questions
- What is the oldest calculator?
- Which machine could add and subtract?
- Which machine could multiply and divide?
- How many beads does a typical abacus row have?
- Who made the Pascaline?
Answers:
- Abacus
- Pascaline
- Leibniz Wheel
- 5 or 2
- Blaise Pascal
FAQ
What was the first calculator made for?
Early calculators were made to help merchants, scientists, and mathematicians do maths faster and more accurately.
Did people use calculators before computers?
Yes! Mechanical calculators were used from the 1600s until the 1900s, long before computers existed.
Can I still buy a mechanical calculator today?
Yes, some shops sell vintage calculators as collectibles, and some are still working.
How did people use these calculators?
People used them to add, subtract, multiply, and divide. They were especially useful for business and science.
Why did people stop using mechanical calculators?
They were replaced by electronic calculators and computers, which are faster and more accurate.