Commission

Learn how salespeople earn commission: find the commission, total earnings with a base salary, the commission rate, the sales needed for a target income and tiered commission.

Intermediate25 min18 problems
Practice Problems

Definition

A commission is money a salesperson earns as a percent of what they sell. The percent is called the commission rate.
Commission is the percent equation you already know, part=rate×whole\text{part} = \text{rate} \times \text{whole}, where the whole is the sales and the part is the commission:
Commission=Commission rate×Sales\text{Commission} = \text{Commission rate} \times \text{Sales}
Many jobs pay a fixed base salary plus commission:
Total earnings=Base salary+Commission rate×Sales\text{Total earnings} = \text{Base salary} + \text{Commission rate} \times \text{Sales}
Example: a shop assistant earns 1,500 dollars a month plus 4% of sales. With sales of 10,000 dollars the commission is 0.04×10,000=4000.04 \times 10{,}000 = 400 dollars, so the total is 1,500+400=1,9001{,}500 + 400 = 1{,}900 dollars.
Always write the rate as a decimal before you multiply: 4%=0.044\% = 0.04.

Try it now

A salesperson earns a 5% commission. Her sales this week are 2,000 dollars. How many dollars of commission does she earn?

Worked Examples

A real estate agent sells a house for 250,000 dollars. Her commission rate is 3%. How much commission does she earn?
1

Write the rate as a decimal

3%=3100=0.033\% = \frac{3}{100} = 0.03
2

Multiply the rate by the sales

0.03×250,000=7,5000.03 \times 250{,}000 = 7{,}500
3

Check with 1%

1%1\% of 250,000250{,}000 is 2,5002{,}500, and 3×2,500=7,5003 \times 2{,}500 = 7{,}500 → Same answer

Common Mistakes

Multiplying by the percent number: 3×250,000=750,0003 \times 250{,}000 = 750{,}000

Why it's wrong: 3% means 3 out of 100, not 3 whole times. The commission can never be bigger than the sales.

Correct: Write the rate as a decimal first: 0.03×250,000=7,5000.03 \times 250{,}000 = 7{,}500

Giving only the commission when the question asks for total earnings

Why it's wrong: Total earnings include the base salary. The commission is only the extra part.

Correct: Total earnings = base salary + commission: 1,800+1,200=3,0001{,}800 + 1{,}200 = 3{,}000

Using the higher tier rate on all sales: 0.08×15,000=1,2000.08 \times 15{,}000 = 1{,}200

Why it's wrong: In tiered commission each rate applies only to its own part of the sales.

Correct: Split the sales: 0.05×10,000+0.08×5,000=500+400=9000.05 \times 10{,}000 + 0.08 \times 5{,}000 = 500 + 400 = 900

Forgetting to subtract the base salary when finding the sales needed: 2,5000.05=50,000\frac{2{,}500}{0.05} = 50{,}000

Why it's wrong: Only the part of the income above the base salary has to come from commission.

Correct: First subtract: 2,500−1,200=1,3002{,}500 - 1{,}200 = 1{,}300, then 1,3000.05=26,000\frac{1{,}300}{0.05} = 26{,}000

Interactive Visual

Bar Chart

Base salary 1,500 + 4% commission

0(1500 dollars)
5,000(1700 dollars)
10,000(1900 dollars)
15,000(2100 dollars)
20,000(2300 dollars)

Ratio Tape Diagram

Up to 10,000: 5%
5000
5000
= 10,000
Above 10,000: 8%
5000
= 5000
Total sales
= 3 (15,000)
If total is:
Up to 10,000: 5% value:10,000
Above 10,000: 8% value:5000

Interactive Sandbox

Expression Calculator

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Practice Problems

18 problems
Problem 1 of 18
Easy
A salesperson earns a 5% commission. Her sales this week are 2,000 dollars. How many dollars of commission does she earn?

Why It Matters

Commission decides the income of millions of people:
  • Real estate agents often earn 2% to 3% of the price of every house they sell
  • Car salespeople usually get a base salary plus a percent of each car sold
  • Shop assistants in electronics or fashion stores often earn a small percent on top of their wage
  • Job offers in sales are hard to compare without math: is 2,000 dollars plus 3% better than 1,400 dollars plus 5%?
Once you can work with commission, you can check a paycheck, set a sales goal and decide which job offer really pays more.

Real World Applications

Real Estate Agents

When a house is sold, the agent who helped sell it is paid a percent of the selling price.

Example:

On a 400,000 dollar apartment with a 2% commission, the agent earns 0.02×400,000=8,0000.02 \times 400{,}000 = 8{,}000 dollars.

1Try It Yourself

An agent sells a house for 320,000 dollars. Her commission rate is 2.5%.

How much commission does she earn, in dollars?

Step 1: Write the mathematical expression

Multiply the selling price by the rate as a decimal:

Comparing Job Offers at a Car Dealership

Sales jobs often mix a fixed base salary with commission. A higher base is safer, a higher rate pays more when sales are good.

Example:

Offer A pays 2,000 dollars plus 3%, offer B pays 1,400 dollars plus 5%. They pay the same when 0.02×sales=6000.02 \times \text{sales} = 600, so at sales of 30,000 dollars. Above that, offer B pays more.

2Try It Yourself

Offer A: 2,000 dollars a month plus 3% of sales. Offer B: 1,400 dollars a month plus 5% of sales. You expect to sell 40,000 dollars a month.

How many dollars more per month does the better offer pay?

Step 1: Write the mathematical expression

Subtract the total of offer A from the total of offer B:

A Shop Assistant's Sales Goal

Shop assistants who earn commission often set a monthly sales target so they reach the income they need.

Example:

With a base of 1,500 dollars and 4% commission, sales of 20,000 dollars give 1,500+800=2,3001{,}500 + 800 = 2{,}300 dollars (see the bar chart).

3Try It Yourself

A shop assistant earns 1,500 dollars a month plus 4% commission. She wants to earn 1,900 dollars this month.

How much must she sell, in dollars?

Step 1: Write the mathematical expression

Divide the commission she needs by the rate:

Key Takeaways

  • 1Commission = commission rate × sales, the percent equation with the sales as the whole
  • 2Always write the rate as a decimal before multiplying: 3%=0.033\% = 0.03, 2.5%=0.0252.5\% = 0.025
  • 3Total earnings = base salary + commission
  • 4Commission rate = commission ÷ sales, then multiply by 100 to get a percent
  • 5Sales needed = (target income - base salary) ÷ rate
  • 6Tiered commission: apply each rate only to its own part of the sales, then add the parts

Frequently Asked Questions

Not quite. Commission is tied to each sale and grows with every dollar sold. A bonus is usually a fixed extra amount paid for reaching a goal.
Not quite. Commission is tied to each sale and grows with every dollar sold. A bonus is usually a fixed extra amount paid for reaching a goal.
No. That would mean the salesperson earns more than the price of what was sold. Real rates are usually between 1% and 20%.
To reward strong sellers. A higher rate above a certain amount makes every extra sale worth more, so salespeople are motivated to sell beyond the first tier.
Compute the total earnings of each offer for the sales you expect. You can also find the break-even sales, where both offers pay the same: below it the higher base salary wins, above it the higher rate wins.

Glossary

Commission
Money earned as a percent of the sales a person makes
Commission rate
The percent of the sales paid as commission, for example 3%
Sales
The total value of what the salesperson sold, the whole in the percent equation
Base salary
A fixed amount paid no matter how much is sold
Total earnings
Base salary plus commission
Tiered commission
A system where different rates apply to different parts of the sales, for example 5% up to 10,000 and 8% above

Formula Card

Commission

Commission=rate×sales\text{Commission} = \text{rate} \times \text{sales}

Write the rate as a decimal first

Total earnings

Earnings=base salary+rate×sales\text{Earnings} = \text{base salary} + \text{rate} \times \text{sales}

Fixed pay plus commission

Commission rate

rate=commissionsales\text{rate} = \frac{\text{commission}}{\text{sales}}

Multiply by 100 to write it as a percent

Sales needed

sales=target−base salaryrate\text{sales} = \frac{\text{target} - \text{base salary}}{\text{rate}}

Sales that give a target income

Today's challengeOne problem, three tries

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