Linear Extrapolation Calculator

What is the Linear Extrapolation Calculator?

The Linear Extrapolation Calculator predicts a performance metric, such as response time, CPU or memory, at a load level you have not tested yet. It draws a straight line through two measurements you already have and extends it. Capacity planners use it to get a quick estimate of how a system might behave at higher load before running an expensive full-scale test.

How it works

Two known (X, Y) measurements define a straight line. This calculator finds that line’s slope and extends it out to a new X value — useful for projecting response time or resource usage at a load level you have not directly tested (used with appropriate caution: real systems are rarely linear far beyond the tested range).

Formula to calculate the extrapolated Y value

Where:

• X1, Y1 — First known measurement, e.g. a load level and its response time.
• X2, Y2 — Second known measurement. X2 must be different from X1.
• (Y2 − Y1) ÷ (X2 − X1) — Slope of the line: how much Y changes per unit of X.
• New X — Load level at which you want to estimate Y.

Example of linear extrapolation

Two load tests have been run, and you want to estimate response time at 150 users.

Inputs

• X1 = 50 users, Y1 = 800 ms
• X2 = 100 users, Y2 = 1400 ms
• New X = 150 users

Step-by-step

1. Slope = (1400 − 800) ÷ (100 − 50) = 12 ms per user
2. Y = 800 + 12 × (150 − 50) = 800 + 1200 = 2000

Common mistakes to avoid

• Extrapolating far beyond the range of the two known points — most systems behave non-linearly once they approach saturation.

• Using two points that are too close together, which amplifies the effect of measurement noise on the slope.

• Treating the result as a guarantee rather than a rough projection worth validating with a real test.