Nonlinear Regression Calculator

Free nonlinear regression calculator. Fit logarithmic, inverse, square-root, and Michaelis-Menten curves with step-by-step solutions, R², and graphs. Browser-based privacy.

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Nonlinear Regression Calculator

Free nonlinear regression calculator. Fit logarithmic, inverse, square-root, and Michaelis-Menten curves with step-by-step solutions, R², and graphs. Browser-based privacy.

Model

Enter your data points

#	X	Y

Results

Equation

R²

Predicted Y

For X = —

Statistics

Statistic	Value
Standard Error
Sample Size (n)
Degrees of Freedom

Chart

Step-by-Step Solution

How to Use This Nonlinear Regression Calculator

Growth & Decay

Fit logarithmic, inverse, square-root, and Michaelis-Menten curves with automatic linearization.

Input Data

Enter paired X and Y values. Minimum 2 points required. Watch model constraints (e.g., x > 0 for log).

Statistical Output

Get model parameters, R², standard error, predictions, and step-by-step transformations.

Choose the simplest model that captures your data. Overly complex models overfit noise.

What Is Nonlinear Regression?

Nonlinear regression fits relationships where the effect of the predictor on the response follows a curved, bounded, or saturating pattern that a straight line cannot capture. Unlike polynomial regression — which bends freely — nonlinear models are chosen because they express known scientific laws.

This calculator supports four common nonlinear models:

Logarithmic — growth slows continuously (e.g., diminishing returns in marketing)
Inverse — response decays with reciprocal distance (e.g., gravity, electrostatic force)
Square Root — effect grows but at a decelerating rate (e.g., resource allocation)
Michaelis-Menten — enzyme kinetics and saturating processes (e.g., reaction rates plateau as substrate concentration rises)

Each model is linearized mathematically so ordinary least squares can be applied, then parameters are transformed back to the original scale.

How Nonlinear Regression Works

1
Select a model: Choose logarithmic, inverse, square-root, or Michaelis-Menten based on the expected shape of your data.
2
Transform the data: Apply a mathematical transformation that converts the nonlinear equation into a straight line. For example, logarithmic regression transforms X to ln(x) and then fits y = a + b·ln(x).
3
Fit ordinary least squares (OLS): Apply linear regression to the transformed variables. The slope and intercept give the parameters of the original nonlinear model.
4
Back-transform parameters: Convert regression coefficients into the natural parameters of the chosen model (e.g., Vmax and Km for Michaelis-Menten).
5
Evaluate on the original scale: Compute predicted values using the original (non-transformed) equation, then calculate R², standard error, and residuals to assess real-world fit.

When to Use Nonlinear Regression

The relationship follows a known physical, biological, or economic law (e.g., enzyme kinetics, inverse-square laws)
Polynomial curves wiggle unrealistically while a simpler nonlinear form captures the trend smoothly
The response naturally saturates, decays, or grows at a decelerating rate
You need parameters with direct scientific meaning (e.g., Vmax, Km, carrying capacity)

When to Avoid Nonlinear Regression

When a simple straight line or low-degree polynomial already explains the data well
When the chosen model’s constraints are violated (e.g., x ≤ 0 for logarithmic, x = 0 for inverse)
When data is sparse — nonlinear models can be unstable with few points
When the true relationship is periodic, oscillatory, or has multiple inflection points not covered by these models

Nonlinear Regression Calculator