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103 LearnersLast updated on September 16, 2025
Linear Interpolation Calculator
Calculators are reliable tools for solving simple mathematical problems and advanced calculations like trigonometry. Whether you’re cooking, tracking BMI, or planning a construction project, calculators will make your life easy. In this topic, we are going to talk about linear interpolation calculators.
What is a Linear Interpolation Calculator?
A linear interpolation calculator is a tool used to estimate the value of a function between two known values. This tool is helpful in predicting values where data points are not explicitly given, making the estimation process much easier and faster, saving time and effort.
How to Use the Linear Interpolation Calculator?
Given below is a step-by-step process on how to use the calculator:
Step 1: Enter the known values: Input the known x and y values into the given fields.
Step 2: Enter the target x-value: Input the x-value for which you want to estimate the y-value.
Step 3: Click on calculate: Click on the calculate button to find the interpolated value.
Step 4: View the result: The calculator will display the estimated y-value instantly.
How to Perform Linear Interpolation?
In order to perform linear interpolation, there is a simple formula that the calculator uses. If you have two points (x1, y1) and (x2, y2), the formula is: \( y = y1 + \frac{(x - x1) \times (y2 - y1)}{x2 - x1} \)
This formula estimates the y-value at a given x by taking the weighted average based on the distance between the known x-values.
Tips and Tricks for Using the Linear Interpolation Calculator
When using a linear interpolation calculator, there are a few tips and tricks to make it easier and avoid mistakes:
Consider the range: Ensure the x-value for interpolation is within the range of the known x-values.
Understand the linearity: Linear interpolation assumes a straight line between points; it may not be accurate for non-linear data.
Use graphical representation: Visualizing the data can aid in understanding and verifying the interpolation.
Common Mistakes and How to Avoid Them When Using the Linear Interpolation Calculator
Even when using a calculator, mistakes can happen. Here are some common mistakes and how to avoid them:
Mistake 1
Misplacing the known values.
Ensure you input the correct known values for x1, y1, x2, and y2. Mixing these up can lead to incorrect results.
Mistake 2
Using values outside the range.
Linear interpolation is only accurate within the known range. Using x-values outside (extrapolation) can lead to unreliable results.
Mistake 3
Ignoring the need for linearity.
Ensure the relationship between data points is approximately linear. Using interpolation on non-linear data can cause significant errors.
Mistake 4
Overrelying on calculator precision.
Remember that interpolation is an estimate. Double-check results for reasonableness, especially in critical applications.
Mistake 5
Assuming perfect accuracy.
Calculators provide an approximation. Always consider the context and potential error margins when interpreting results.
Linear Interpolation Calculator Examples
Problem 1
A company recorded sales of $200 in January and $300 in March. Estimate the sales in February.
Using the formula: \(y = y1 + \frac{(x - x1) \times (y2 - y1)}{x2 - x1} \)
Let January = 1, February = 2, March = 3,
so: \(y = 200 + \frac{(2 - 1) \times (300 - 200)}{3 - 1} y = 200 + \frac{1 \times 100}{2} = 250\)
Estimated sales in February are $250.
Explanation
By substituting the known values into the interpolation formula, we interpolate February sales as $250 between January and March sales.
Problem 2
A car travels 100 km in 2 hours and 150 km in 3 hours. Estimate the distance traveled in 2.5 hours.
Using the formula: \(y = y1 + \frac{(x - x1) \times (y2 - y1)}{x2 - x1}\)
Let 2 hours = 100 km and 3 hours = 150 km,
so: \(y = 100 + \frac{(2.5 - 2) \times (150 - 100)}{3 - 2} \)
\(y = 100 + \frac{0.5 \times 50}{1} = 125 \)
Estimated distance is 125 km in 2.5 hours.
Explanation
By applying the interpolation formula, we estimate that the car travels 125 km in 2.5 hours, between the recorded distances.
Problem 3
A temperature reading was 20°C at 1 PM and 30°C at 3 PM. Estimate the temperature at 2 PM.
Using the formula:\( y = y1 + \frac{(x - x1) \times (y2 - y1)}{x2 - x1} \)
Let 1 PM = 20°C and 3 PM = 30°C,
so: \( y = 20 + \frac{(2 - 1) \times (30 - 20)}{3 - 1} \)
\( y = 20 + \frac{1 \times 10}{2} = 25 \)
Estimated temperature at 2 PM is 25°C.
Explanation
The interpolation formula gives us an estimate of 25°C for the temperature at 2 PM, based on the known values.
Problem 4
A plant grows 5 cm in 10 days and 15 cm in 20 days. Estimate its height after 15 days.
Using the formula: \(y = y1 + \frac{(x - x1) \times (y2 - y1)}{x2 - x1} \)
Let 10 days = 5 cm and 20 days = 15 cm,
so: \(y = 5 + \frac{(15 - 10) \times (15 - 5)}{20 - 10} \)
\( y = 5 + \frac{5 \times 10}{10} = 10 \)
Estimated height after 15 days is 10 cm.
Explanation
By applying linear interpolation, we find that the plant's estimated height after 15 days is 10 cm.
Problem 5
A runner completes 5 km in 20 minutes and 10 km in 40 minutes. Estimate the distance after 30 minutes.
Using the formula: \(y = y1 + \frac{(x - x1) \times (y2 - y1)}{x2 - x1} \)
Let 20 minutes = 5 km and 40 minutes = 10 km,
so: \( y = 5 + \frac{(30 - 20) \times (10 - 5)}{40 - 20} \)
\( y = 5 + \frac{10 \times 5}{20} = 7.5 \)
Estimated distance after 30 minutes is 7.5 km.
Explanation
Using the interpolation formula, the runner is estimated to have covered 7.5 km in 30 minutes.
FAQs on Using the Linear Interpolation Calculator
1.How do you calculate linear interpolation?
2.Is interpolation only accurate within a certain range?
3.Why is linear interpolation useful?
4.How do I use a linear interpolation calculator?
5.Is the linear interpolation calculator accurate?
Glossary of Terms for the Linear Interpolation Calculator
- Linear Interpolation: A method of estimating unknown values between two known values using a straight line.
- Extrapolation: Estimating values outside the range of known data points, often less reliable than interpolation.
- Weighted Average: A method of calculating averages where different values are given different levels of importance.
- Linearity: The property of a relationship being represented as a straight line.
- Estimate: An approximate calculation or judgment, often used when exact data is not available.
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Seyed Ali Fathima S
About the Author
Seyed Ali Fathima S a math expert with nearly 5 years of experience as a math teacher. From an engineer to a math teacher, shows her passion for math and teaching. She is a calculator queen, who loves tables and she turns tables to puzzles and songs.
Fun Fact
: She has songs for each table which helps her to remember the tables
