Linear Interpolation Calculator with Formula & Examples Linear interpolation is a simple method to estimate values between two known points. Imagine you know the price of a house in 2020 and 2024. Linear interpolation helps you guess the price in 2022 by drawing a straight line between those two years.
This guide explains the linear interpolation formula, shows a step-by-step example, and provides a Python tool to calculate values instantly. The Linear Interpolation Formula The formula finds an unknown -value for a given -value that sits between two known points,
y=y1+(x−x1)(y2−y1)x2−x1bold y equals bold y sub 1 plus the fraction with numerator open paren bold x minus bold x sub 1 close paren open paren bold y sub 2 minus bold y sub 1 close paren and denominator bold x sub 2 minus bold x sub 1 end-fraction What the Symbols Mean: x1,y1bold x sub 1 comma bold y sub 1
: The coordinates of your first known data point (lower bound). x2,y2bold x sub 2 comma bold y sub 2
: The coordinates of your second known data point (upper bound). : The independent value you want to interpolate. : The estimated dependent value you want to find. Step-by-Step Practical Example
Let us look at a real-world scenario to see how the formula works.
A local bakery tracks its daily revenue based on the number of customers. On a day with 10 customers ( ), they make ₹1,500 ( ). On a day with 30 customers ( ), they make ₹3,500 ( ). How much revenue ( ) will they likely make on a day with 18 customers ( )? Calculation Steps: Identify your values: Plug them into the formula:
y=1500+(18−10)(3500−1500)30−10y equals 1500 plus the fraction with numerator open paren 18 minus 10 close paren open paren 3500 minus 1500 close paren and denominator 30 minus 10 end-fraction Simplify the brackets:
y=1500+(8)(2000)20y equals 1500 plus the fraction with numerator open paren 8 close paren open paren 2000 close paren and denominator 20 end-fraction Solve the fraction: y=1500+1600020y equals 1500 plus 16000 over 20 end-fraction y=1500+800y equals 1500 plus 800 Final Result: y=2300y equals 2300 If 18 customers visit, the estimated revenue is ₹2,300. Interactive Python Calculator
You can use this simple script to calculate linear interpolation automatically. Copy and run this code in any Python environment.
def linear_interpolation(x1, y1, x2, y2, x): # Ensure we don’t divide by zero if x2 == x1: return “Error: x2 and x1 cannot be the same value.” # Apply the formula y = y1 + ((x - x1)(y_2 - y_1)) / (x2 - x1) return y # Example Data Input known_x1 = 10 known_y1 = 1500 known_x2 = 30 known_y2 = 3500 target_x = 18 # Run the calculation result = linear_interpolation(known_x1, known_y1, known_x2, known_y2, target_x) print(f”The interpolated y-value for x = {target_x} is: {result}“) Use code with caution. Common Applications Data Science: Filling in missing gaps in datasets.
Engineering: Reading values from steam tables or material stress graphs. Animation: Creating smooth movement between two keyframes.
If you have a specific dataset you are working on, let me know. I can help by calculating the missing values, writing a custom Excel formula for your sheet, or explaining how to handle data points that fall outside the range (extrapolation).
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