How to Find the Dependent & Independent Variables (With Examples)

Whether you’re conducting a science experiment or learning algebra, you’re going to deal with variables. Independent and dependent variables are 2 important concepts that help you understand the relationship between the things you’re measuring. In this article, we’ll explain the difference between independent and dependent variables and how to tell them apart with examples and help from scientific researcher Dr. Michael Simpson, PhD. We’ll also explain how to find these variables in an equation and graph them, too. Read on to learn more!

Dependent vs. Independent Variables

Dependent variables are affected by and depend on other variables, according to scientific researcher Dr. Michael Simpson. They’re usually the outcome you’re measuring. Independent variables are not affected by other variables. They’re what you manipulate or change in an experiment to cause an effect.

Section 1 of 6:

What are independent and dependent variables?

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1
The independent variable is the cause that produces an effect. The independent variable isn’t affected or influenced by other variables in a study, says Dr. Simpson. In a scientific experiment, this is the variable that changes or that a researcher manipulates to see how it affects another variable. ^{[1]
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Expert Source

Michael Simpson, PhD
Registered Professional Biologist

Expert Interview. 25 June 2021.}
- The independent variable is often called the manipulated, experimental, explanatory, or predictor variable.
- There are 2 types of independent variables :
  - Experimental variables can be manipulated by a researcher. These include variables like medication dosage.
  - Subject variables can’t be manipulated by a researcher. These include variables like age, race, gender identity, and income level.
- Examples :
  - If a researcher wants to see how well different doses of a medication work, the dose is the independent variable.
  - If you want to see if studying more improves your test scores, the amount of time you spend studying is the independent variable.
2
The dependent variable is the outcome you’re measuring. The dependent variable is affected or changed by the independent variable; it always depends on another factor. According to Dr. Simpson, “the dependent variables are the responses that you measure…the results you get will be based on the independent variable.” This variable is usually the focus of the study—the goal of an experiment is to explain or predict the dependent variable caused by the independent variable. ^{[2]
X
Expert Source

Michael Simpson, PhD
Registered Professional Biologist

Expert Interview. 25 June 2021.}
- The dependent variable is often called the response or outcome variable.
- Examples :
  - If a researcher is testing an allergy medication, the allergy relief after taking the dose is the dependent variable (the outcome caused by taking the medicine).
  - If you’re examining whether study time improves your test scores, the grade you receive is the dependent variable.

Section 2 of 6:

Determining If a Variable is Independent or Dependent

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When distinguishing between variables, ask yourself if it makes sense to say one leads to the other. Since a dependent variable is an outcome, it can’t cause or change the independent variable. For instance, “Studying longer leads to a higher test score” makes sense, but “A higher test score leads to studying longer” is nonsense. ^{[3]
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Tip: When you encounter variables, plug them into this sentence : “Independent variable causes Dependent Variable, but it isn't possible that Dependent Variable could cause Independent Variable.

For example: “A 5 mg dose of medication causes allergy relief, but it isn’t possible that allergy relief could cause a 5 mg dose of medication.”
2
Ask which variable is being changed to find the independent variable. Whether you’re reading a word problem or a scientific study, remember that the independent variable is not affected by other variables; it is the cause that produces an effect. There are a few questions you can ask yourself to help identify the independent variable: ^{[4]
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- Which variable changes, is being manipulated, or is being used as a factor to group subjects (like age or race)?
- Which variable is being used to understand how it affects another?
- Which variable causes an effect in another, or which variable comes before the other?
3
Determine which variable is being measured to find the dependent variable. Keep in mind that the dependent variable is influenced by other variables and is usually the outcome you’re measuring. To help yourself identify the dependent variable in a math problem or research study, ask: ^{[5]
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- Which variable is dependent on another variable, or which variable is being affected or changed by another?
- Which variable is being measured as an outcome or effect?
- Which variable is being measured after another variable is changed?

Section 3 of 6:

Examples of Independent and Dependent Variables

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Look at these examples to identify independent and dependent variables. One of the best ways to understand the difference between independent and dependent variables is to look at different research study questions. Use these questions to test your knowledge—don’t worry, we’ll provide the answers, too!
- How tall does a plant grow under different fertilizer concentrations?
  - Independent variable : The fertilizer concentration. Dr. Simpson says “the amount of fertilizer you give…is an independent variable because it is not influenced by (or it is independent of) anything.” ^{[6]
    X
    Expert Source
    
    Michael Simpson, PhD
    Registered Professional Biologist
    
    Expert Interview. 25 June 2021.}
  - Dependent variable : The plant’s height. According to Dr. Simpson, “Height is your dependent variable because…it is dependent on fertilizer concentration.” ^{[7]
    X
    Expert Source
    
    Michael Simpson, PhD
    Registered Professional Biologist
    
    Expert Interview. 25 June 2021.}
- How do different amounts of sleep impact test performance?
  - Independent variable : Hours of sleep you get each night. This is the variable you’re manipulating to see how it affects another.
  - Dependent variable : The score on a test. This is the variable that’s affected by sleep and what you’re measuring.
- Does more time spent in the sun improve people’s mood?
  - Independent variable : Time spent in the sun. You’re changing how many hours of sun someone is exposed to.
  - Dependent variable : Mood. You’re measuring how someone’s mood is affected by how much sun exposure they receive.
- Do younger or older adults have a better attention span?
  - Independent variable : Age. This is the variable that is being changed in the study to assess an effect.
  - Dependent variable : Attention span. This is the variable that you’re measuring to see how it’s affected by age.

Section 4 of 6:

Identifying Independent and Dependent Variables in Equations

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1
Use letters to represent variables in word problems. Turning statements with variables into math equations makes it easy to see which variable is which. For example, suppose your parents give you $3 for every chore you complete. You want to figure out how much you'll earn if you do a certain number of chores. ^{[8]
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- The $3 per chore is a constant. Your parents set that in stone, and that number isn't going to change.
- On the other hand, the number of chores you do and the total amount of money you earn aren't constant. They're variables that you want to measure.
- To set up an equation, use letters to represent the chores you do and the money you'll earn. Let t represent the total amount of money you earn and n stand for the number of chores you do.
2
Set up an equation with the variables. If you get $3 for every chore you complete, say out loud, “The total amount of money I'll earn (or t ) equals $3 times the number of chores I do (or n ).” That gives you the equation t = 3n . ^{[9]
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- Notice that the amount of money you'll earn depends on the number of chores you do. Since it depends on other variables, it's the dependent variable .
3
Practice solving equations to see how variables are connected. If, in the chores example, t = 3n and you do 5 chores, then t = (3)(5) = 15 . Doing 5 chores causes t to equal $15, so t depends on n . ^{[10]
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- Example : Say an episode of your favorite TV show is 30 minutes. The total time in minutes ( m ) you'll spend watching TV equals 30 times the number of episodes ( e ) you watch. That gives you the equation m = 30e . If you watch 3 episodes, m = (30)(3) = 90 .
4
Plug different values into the independent variable. Remember that, in an experiment, a researcher changes the independent variable to see how it affects other variables, says Dr. Simpson. ^{[11]
X
Expert Source

Michael Simpson, PhD
Registered Professional Biologist

Expert Interview. 25 June 2021.} Equations work the same way! Try solving your practice equations using different numbers for the independent variables. ^{[12]
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- Example : Say you want to know how much you'll earn if you do 8 chores instead of 5. Plug 8 into n : t = (3)(8) = 24 . It's the same principle as a researcher changing the dose of a medication from 2 mg to 4 mg to test its effects.

Section 5 of 6:

Graphing Independent and Dependent Variables

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1
Put independent variables on the x-axis and dependents on the y-axis. Draw a vertical line, which is the y-axis. Then make the x-axis, or a horizontal line that goes from the bottom of the y-axis to the right. The y-axis represents a dependent variable, while the x-axis represents an independent variable. ^{[13]
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- Example : Say you sell apples and want to see how advertising affects your sales. The amount of money you spent in a month on advertising is the independent variable, or the factor that causes the effect you’re trying to understand. The number of apples you sold that month is the dependent variable.
- Note : You usually use line graphs to visualize quantitative data or show changes over time, while bar graphs are usually used to graph discrete categories (like age). ^{[14]
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2
Label the x-axis with units to measure your independent variable. Make dashes in even increments along the horizontal line. The line should now look a bit like a ruler. These dashes will stand for units, which you’ll use to measure your independent variables. ^{[15]
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- Example : Suppose you’re trying to see if advertising more increases the number of apples you sold. Divide the x-axis into units to measure your monthly advertising budget.
- If you’ve spent between $0 and $500 a month in the last year on advertising, draw 10 dashes along the x-axis. Label the left end of the line “$0.” Then, label each dash with a dollar amount in $50 increments ($50, $100, $150, and so on) until you’ve reached the last dash, or “$500.”
3
Draw dashes along the y-axis to measure the dependent variable. As with the x-axis, make dashes along the y-axis to divide it into units. If you're studying the effects of advertising on your apple sales, the y-axis measures how many apples you sold per month. ^{[16]
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- Example : Suppose your monthly apple sales have ranged between 60 and 250 over the last year. Draw 10 dashes across the y-axis, label the first “50,” and label the rest of the dashes in increments of 25 (50, 75, 100, and so on), until you’ve written 275 next to the last dash.
4
Enter your variables' coordinates onto the graph. Use your variables’ number values as coordinates, and place a dot on the corresponding point on your graph. The coordinate is where invisible lines running from the x and y-axes cross each other. ^{[17]
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- Example : If you spent $350 on advertising last month, find the dash labeled “350” on the x-axis. If last month’s apple sales totaled 225, find the dash labeled “225” on the y-axis. Draw a dot at the point on the graph coordinate ($350, 225), then continue graphing points for the rest of your monthly numbers.
5
Look for patterns in the points you’ve graphed. If the dots form a recognizable pattern, such as a roughly organized line, there’s a relationship between the independent and dependent variables. The independent variable probably doesn’t affect the dependent variable if the dots are randomly scattered across the graph without any recognizable order. ^{[18]
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- Example : Say you’ve graphed your advertising expenses and monthly apple sales, and the dots are arranged in an upward sloped line. This means that your monthly sales were higher when you spent more on advertising.

Section 6 of 6:

Summary

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The independent variable is the cause and the dependent is the outcome. The independent variable is the variable that is manipulated or changed in a study; it is not affected by other variables. On the other hand, the dependent variable is affected or changed by other variables; it is often the outcome you’re measuring in the study.
- Remember that the independent variable can affect the dependent variable, but the dependent variable cannot affect the independent variable.
- Essentially, the independent variable is the cause, and the dependent variable is the effect.

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Question

What are dependent and independent variables in a study?

Michael Simpson, PhD
Scientific Researcher
Dr. Michael Simpson (Mike) is a Registered Professional Biologist in British Columbia, Canada. He has over 20 years of experience in ecology research and professional practice in Britain and North America, with an emphasis on plants and biological diversity. Mike also specializes in science communication and providing education and technical support for ecology projects. Mike received a BSc with honors in Ecology and an MA in Society, Science, and Nature from The University of Lancaster in England as well as a Ph.D. from the University of Alberta. He has worked in British, North American, and South American ecosystems, and with First Nations communities, non-profits, government, academia, and industry.

Michael Simpson, PhD

Scientific Researcher

Expert Answer

In a study design, the dependent variables are the responses that you measure on, in or around the subjects you are studying. The results you get will be based on the independent variable.

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What is the main difference between dependent and independent variables?

Michael Simpson, PhD
Scientific Researcher
Dr. Michael Simpson (Mike) is a Registered Professional Biologist in British Columbia, Canada. He has over 20 years of experience in ecology research and professional practice in Britain and North America, with an emphasis on plants and biological diversity. Mike also specializes in science communication and providing education and technical support for ecology projects. Mike received a BSc with honors in Ecology and an MA in Society, Science, and Nature from The University of Lancaster in England as well as a Ph.D. from the University of Alberta. He has worked in British, North American, and South American ecosystems, and with First Nations communities, non-profits, government, academia, and industry.

Michael Simpson, PhD

Scientific Researcher

Expert Answer

The difference between independent and dependent variables is essentially the difference between cause and effect. For example, if you are studying the growth of a plant species under different fertilizer concentrations, you might choose height as your variable if your hypothesis is that fertilizer concentration affects plant height. Height is your dependent variable because, according to your hypothesis, it is dependent on fertilizer concentration.

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What is the independent and dependent variable for y+5 = x^2 / 3+1?

Donagan

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The variable that is expressed in the first degree (having an exponent of 1) is the dependent variable. In this case, it's y.

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How to Find the Dependent & Independent Variables (With Examples)

Dependent vs. Independent Variables

Steps

What are independent and dependent variables?

Determining If a Variable is Independent or Dependent

Examples of Independent and Dependent Variables

Identifying Independent and Dependent Variables in Equations

Graphing Independent and Dependent Variables

Summary

Expert Q&A

Video

Tips

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