Calculate interpolated values between two points using linear interpolation. Perfect for mathematics, engineering, and data analysis applications.
Comprehensive interpolation calculations with detailed explanations
Calculate interpolated values between two known points
Calculate slope and linear equation from data points
Analyze multiple data points and find interpolated values
Detailed explanations and calculation steps
Understanding linear interpolation and its applications
Input two known points or multiple data points for interpolation.
Enter the x-value for which you want to find the interpolated y-value.
Receive interpolated value, slope, equation, and step-by-step calculations.
y = y₁ + (y₂ - y₁)(x - x₁)/(x₂ - x₁)
m = (y₂ - y₁)/(x₂ - x₁)
y = mx + b
Common interpolation calculations and their practical applications
Result: y = 3
Result: y = 6
0°C→32°F, 100°C→212°F, 25°C = 77°F
0s→0m, 10s→50m, 5s = 25m
Common questions about linear interpolation
Linear interpolation is a method to estimate values between two known data points by assuming a linear relationship. It's used to find intermediate values when you have two points on a line.
Linear interpolation uses the formula: y = y₁ + (y₂ - y₁)(x - x₁)/(x₂ - x₁), where (x₁, y₁) and (x₂, y₂) are the two known points, and x is the value you want to interpolate.
Use linear interpolation when you need to estimate values between two known points, when dealing with linear relationships, or when you need a quick approximation for data analysis.
Linear interpolation assumes a linear relationship between points. It may not be accurate for non-linear data, and accuracy decreases with larger gaps between data points.
Yes, with multiple data points, you can find the two closest points to your target value and use them for linear interpolation. This is called piecewise linear interpolation.
Interpolation estimates values between known data points, while extrapolation estimates values beyond the known data points. Interpolation is generally more accurate than extrapolation.
Linear interpolation accuracy depends on how linear the actual relationship is between data points. It's most accurate when the relationship is truly linear and points are close together.
Linear interpolation is used in engineering, data analysis, computer graphics, scientific computing, temperature conversions, and many other fields where intermediate values need to be estimated.
While linear interpolation assumes linear relationships, it can still provide reasonable approximations for non-linear data over small intervals, though the accuracy will be reduced.
The slope (m) in linear interpolation is calculated as: m = (y₂ - y₁)/(x₂ - x₁), where (x₁, y₁) and (x₂, y₂) are the two known points.
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