How does the Tangent Line Calculator work?

Find derivative f'(x) of function Then: Evaluate slope m = f'(x₀) at point x₀ Then: Use point-slope form: y - y₀ = m(x - x₀) Then: Simplify to slope-intercept form.

Can you give an example of how to use the Tangent Line Calculator?

Example: Input y=x^2, point (2,4) gives a result of y=4x-4.

Is the Tangent Line Calculator free to use?

Yes — completely free with no registration, download, or subscription required. All calculations happen instantly in your browser.

How accurate is the Tangent Line Calculator?

Our Tangent Line Calculator uses verified mathematical formulas and is accurate to multiple decimal places. Results are calculated in real-time using the same methods used by professionals.

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Tangent Line Calculator

Tangent Line to Circle

Circle center h

Circle center k

Circle radius (r)

External point x

External point y

Finds tangent line to curve at a point using calculus (derivative).

Symbol	Name	Unit	Description
m	f\'(x₀) at point x₀	—	f\'(x₀) at point x₀

Difficulty:advanced

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Did You Know?

Tangent line best linear approximation to curve; used in Newton's method for root-finding.

References

›Tangent Line Calculator

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Tangent Line Calculator

Tangent Line to Circle

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Tangent Line to Circle