Interpolation Calculator – Linear and Polynomial Tool
Use this interpolation calculator to find unknown values between two known data points using linear or polynomial interpolation methods. Perfect for students, engineers, and analysts.
Interpolation Result
For x = 0, the interpolated y value is:
Calculation Explanation
How Linear Interpolation Works
Linear interpolation is the simplest method for estimating values between two known data points. It assumes that the change between two points is linear and follows a straight line. This method is widely used in mathematics, engineering, and computer graphics for its simplicity and efficiency.
The formula for linear interpolation is:
y = y₁ + ((x – x₁) × (y₂ – y₁)) / (x₂ – x₁)
Where (x₁, y₁) and (x₂, y₂) are the known data points, and x is the target value for which we want to find the corresponding y value.
When to Use Polynomial Interpolation
Polynomial interpolation creates a polynomial that passes exactly through a set of points. While linear interpolation uses a first-degree polynomial (straight line), polynomial interpolation can use higher-degree polynomials to fit more complex curves.
For two points, polynomial interpolation reduces to linear interpolation. However, when you have three or more points, polynomial interpolation can provide a more accurate curve that passes through all points.
This method is particularly useful when you suspect the relationship between variables is non-linear, such as in physical simulations, economic forecasting, and engineering design.
Applications in Engineering, Data Science & Finance
Engineering: Interpolation is essential in engineering for reading values from charts and tables, such as steam tables, material property data, and calibration curves. It’s also used in computer-aided design (CAD) and computer graphics for rendering curves.
Data Science: In data analysis, interpolation fills missing values in datasets, creates smooth visualizations, and helps in resampling time series data. Machine learning models often use interpolation for feature engineering.
Finance: Financial analysts use interpolation to estimate yield curves, calculate bond prices between coupon dates, and determine implied volatilities for options pricing. It’s also used in forecasting and risk management models.
Frequently Asked Questions
What is an interpolation calculator?
An interpolation calculator is a tool that estimates missing values between two data points using mathematical formulas. It helps users find intermediate values without performing complex calculations manually.
What is the formula for linear interpolation?
The standard formula for linear interpolation is: y = y₁ + ((x – x₁) × (y₂ – y₁)) / (x₂ – x₁). This formula calculates the y value corresponding to a given x value between two known points (x₁, y₁) and (x₂, y₂).
Can I use this for finance or science?
Yes, interpolation is widely applicable in physics, statistics, engineering, and economics. It’s used in financial modeling, scientific data analysis, engineering design, and various research applications where estimation between data points is needed.
Is this tool accurate?
For 2-point interpolation, this calculator provides exact formulaic results based on the input values. However, accuracy depends on the appropriateness of the interpolation method for your data and the assumption of linearity between points.
Disclaimer
This calculator is intended for estimation and educational purposes. Results should be verified with professional methods when used in critical applications. The creators are not liable for decisions made based on calculations from this tool.