How to count back change without a calculator

One of the easiest, most helpful “adulting” skills to learn is counting back change. So few people can do it now, supposedly, so you could really impress with this.

I picture two people in their early 20s sitting at a table on a date, one wanting to be impressed and the other saying, “You know, I can count back change without a calculator.” They pull out $1 bills and coins to demonstrate and teach.

I’m not being facetious here. As an autistic who knows several useless facts out of context and feels she is mediocre at most “impressive” things, being able to impress people with my ability to count back change without a calculator would be so easy.

I don’t date, though. I want other things in my life more than a life partner, so I don’t actively look or anything. 🤷‍♀️

Also, also, ALSO: This definitely works for US currency. I have no idea how other currencies work or if this would allow for it, but I imagine it would be similar.

Be familiar with the currency

In the US, there are six coins currently in circulation:

1. Penny: one cent (1¢)
2. Nickel: five cents (5¢)
3. Dime: 10 cents (10¢)
4. Quarter: 25 cents (25¢)
5. Half-dollar: 50 cents (50¢)
6. Dollar: 100 cents (100¢)

The half-dollar and dollar coins are far less common, so I will only be using the first four coins in my examples.

The US has seven paper bills in rotation: $1, $2, $5, $10, $20, $50, $100.

$2 bills are considered “rare”, so I will not be referencing it in my examples. If I say $2 in this post, I mean two $1 bills (though you could use a $2 bill if you had one).

Thinking backwards

Let’s train your brain to think like a cash register!

We’re gonna use patterns here, sort of.

• Think in 5s and 10s.
• A whole number is a number without a decimal, e.g. a full dollar amount”.

The goal of every example in this post is to get your brain doing maths without realizing it’s doing maths. People do maths every single day, all the time, without being consciously aware of it.

• How many plates do you grab for dinner? How do you know to grab that many?
• How many pairs of socks do you need for your feet? Why?

The maths we’ll use in my examples are similar to the maths used to read a mechanical clock — the circle kind.

One hour is 60 minutes. A clock divided into fourths is 15 minutes, therefore 60 divided by 4 is 15.

When an hour is at 50 minutes, we know there are 10 minutes until the next hour because 60-50=10.

Subtraction is like doing maths backwards sometimes. Counting change back is backwards maths because you’re starting with the final answer (the money given to you) and need to sort out the equation.

Basically, you’re solving for x without all the complicated parentheses to it.

Decimals

Decimals in a money amount (in the US) means coins.

If we have 33¢, how many cents do we need to reach 40¢?It’s faster to think how far away we are from the nearest 5 multiple than the nearest 10.2¢ makes 35¢.

From there, we can think of the nearest 10, which is 40¢. 40-35 is 5¢.

In total, we need 7¢ to raise 33¢ to 40¢.

Full dollars

We can think of full dollar maths similarly.

If I have $12, how many more do I need to make $50?

1. Start with $12. How many away from $15? $3.
2. Now we have $15. How many aware from $20? $5.
3. Now we have $20. How many away from $50? $30.

Add it all up, and you have $38.

Solving with currency

Now that you have an idea of how to calculate it, let’s look at translating these amounts into currency.

When counting back change, choose the most efficient route — that is, choose the fewest coins from the ones you have. This is why we think backwards when counting out change.

My first example with coins only was 33¢ needing to get to 40¢. The answer was 7¢. In coins, this can look like

1. 7 pennies
2. 2 pennies (2¢), 1 nickel (5¢)

Which is the most efficient choice? B. 2 pennies and 1 nickel.

If you only have pennies and no nickel, then 7 pennies is your only option.

My second example used full dollars. I had $12 and needed to make $50. The answer was $38. In cash, this can look like:

1. 38 $1 bills
2. Three $1 bills, one $5 bill, one $10 bill, one $20 bill
3. Eight $1 bills, three $10 bills
4. Eight $1 bills, one $10 bill, one $20 bill

B is the most efficient choice because it uses the fewest bills.

Putting it together

Here’s where it gets tricky.

If the total is $3.74 and you only have $5, how much should you receive as change — and in approximately what way?

1. Start with 74¢. How much to 75¢? 1¢, or the value of a penny.
2. Now we have 75¢. How much to 80¢? 5¢, the value of a nickel.
3. Now we have 80¢. How much to $1? 20¢, the value of two dimes.
4. We can exchange the two dimes and nickel for a quarter. That’s more efficient.
5. Look at our total vs. change: the change we calculated plus our total adds up to $4.
6. So now we have $4. How much until $5? $1.

That makes the change $1.26. The most efficient change would be:

• One $1 bill
• One quarter
• One penny

Examples

Let’s solve some examples together.

$65.76 with a $100 bill

1. Start with 76¢. How far away is 80¢? 4¢.
2. Now we have 80¢. How far away from the nearest dollar? 20¢.
3. 24¢ added to $65.76 makes $66.
4. Now we have $66. How much to $70? $4.
5. Now we have $70. How much to $100? $30.

The total change owed is $34.24. The most efficient change would be

• One $20 bill
• One $10 bill
• Two dimes (10¢)
• Four pennies (4¢)

When a register is extremely busy, they may instead round the four pennies up to the nearest 10. So in this case, you might instead receive a quarter.

A similar occurrence happens when someone’s change ends in a 9…especially if it’s 99¢ change owed. Instead of counting it all out, a busy cashier may instead give you $1 change for 99¢ change owed — or round up to the nearest 10 multiple equivalent (e.g. 49¢ owed = 50¢ = two quarters).

Counting out a lot of change is time-consuming, so rounding up may be more efficient. It also may lead to drawers that are “short”. Drawers that are “long” (have more money than it should) may be the result of badly counting out change or putting tips into the register, e.g. when customers say to “keep the change”).

I’m not recommending or dismissing the practice; I’m only teaching you how to count money and explaining the nuances. 💅

$9.53 with $20.75

Sometimes customers have change to hand over as well as cash, but don’t have the exact cash.

In this case, the customer gives one $20 bill and three quarters (75¢) for the total of $9.53.

Let’s solve it together starting with the change. The customer gave 75¢, so we only need to go that far.

1. Start with the change: 53¢. How much to 55¢? 2¢.
2. Now we have 55¢. How much to 60¢? 5¢.
3. Now we have 60¢. How much to 70¢? 10¢.
4. Now we have 70¢. How much to 75¢? 5¢.

Altogether, the coins add up to 22¢. The most efficient change is

• 2 pennies (2¢)
• 2 dimes (20¢)

As for the cash, we can solve it normally since our change is accounted for and does not get added to the total to round up to the nearest dollar amount:

1. We have $9. How much to $10? $1.
2. Now we have $10. How much to $20? $10.

The total cash is $11. The most efficient paper currency expression is:

• One $1 bill
• One $10 bill

Altogether, the change back to the customer is $11.22, expressed as

• One $10 bill
• One $1 bill
• Two dimes
• Two pennies

$50.17 with $60.38

Sometimes, customers have pennies they’re trying to rid themselves of or hang over whatever change is in their pocket…and it’s not even an amount that makes any sense??

Because you’re going to wind up giving them some of it back anyways.

Let’s break this one down by first calculating the coin change:

1. The original total in coins is 17¢. How much to 20¢? 3¢.
2. Now we have 20¢. How much to 30¢? 10¢.
3. Now we have 30¢. How much to 35¢? 5¢.
4. Now we have 35¢. How much to 38¢? 3¢.

The total change in coins is 21¢. The most efficient change in coins is

• Two dimes
• One penny

Now, the cash: We have $50. How much to $60? $10.

Therefore, the total change back is $10.21, using

• One $10 bill
• Two dimes
• One penny

$37.64 with $42.75

In this case, the customer has two $20 bills and two $1 bills, plus three quarters. If you’re unfamiliar with counting change, this seems strange and like “too much”.

It’s still “too much”, but in a different kind of way. Less change would be to only give you two $20 bills ($40).

However, this is a great way to break their bigger bills without asking to trade you ones for a five.

Let’s solve the change first; we need only to reach 75¢ instead of the full dollar amount.

1. Start with 64¢. How much to 65¢? 1¢ or a penny.
2. Now we have 65¢. How much to 70¢? 5¢.
3. Now we have 70¢. How much to 75¢? 5¢.

They only need 11¢ in change, or one dime and one penny.

Now the cash:

1. We have $37. How much to $40? $3.
2. We have $40. How much to $42? $2.

The total cash is $5. Instead of giving them back five $1 bills, we can give them one $5 bill.

The total change is $5.11, which is most efficiently expressed as

• One $5 bill
• One dime
• One penny

$22.59 with $52.60

This example is similar to the previous, in that the customer gave $2 “extra”, but the change is completely different.

The customer also provided 60¢ in coins, which provides easy maths: 60-59=1, so they only need a penny back.

In this case, they gave you a $50 bill and two $1 bills.

The cash part of the total is $22, and you have $52. Subtract $2 from $22, and you have $20.

$50-$20=$30. Therefore, the change is only $30.01.

BUT LET’S LOOK AT IT as if they gave you $50.60 only:

1. We already solved the coins — it’s 1¢, or a penny.
2. We have $22. How much to $25? $3.
3. We have $25. How much to $30? $5.
4. We have $30. How much to $40? $10.
5. We have $40. How much to $50? $10.

The total cash change is $28. This is most efficiently expressed by

• Two $20 bills
• One $5 bill
• Three $1 bills

Whereas, with $30 change, it could be two $20 bills and one $10 bill — three less bills than if they hadn’t given you $2 extra. The $2 allowed you to consolidate the change, even though it was $2 more, by giving you in $1 bills the amount to the nearest 5 or 10 multiple.

If customers give you change, but not enough

Sometimes customers had over whatever change they have, but it’s not enough to round up. (e.g. a $50.17 total and giving you $60.15) I absolutely hate when this because it leads to MORE change, since they end up needing it BACK.

In that case, I’d set their coins aside and give it back with their actual change…or I’d put it in the drawer and condense it into less change to make it look like I “worked” and actually calculated it.

I understand wanting to get rid of your change, but not giving enough is not helpful.

It’s far better in that case to give 2¢ or nothing at all. By giving 2¢ (the pennies), you’re removing the necessity for them to give you any change.

How much change to carry on yourself for exact change

If you want to be able to hand over the exact cash amount, you only need these 10 coins:

• 3 quarters (75¢)
• 1 dime (10¢)
• 2 nickels (5¢)
• 4 pennies (4¢)

You can create any number between 1-99 with this change and not receive any (or much) change in return.

This is the absolute minimum that, if you have a supply of coins, can be “restocked” in your wallet/purse on the regular.

---

The more you practice, the more automatic your brain starts thinking about it. Mental maths are much easier when simplified into multiples of 5 and 10.

Give it a go for yourself in the comments! Some exercises for you:

• Total: $1.37; customer gives you $5.40
• Total: $54.24; customer gives you $100
• Total: $27.40; customer gives you $32.40
• Total: $5.34; customer gives $11