Tangent Line Calculator

The tangent line is the straight line that grazes a curve at a single point while matching its direction exactly, and this calculator finds its equation for any function at any point you choose. Enter a function of x and the x-value of the point, and it returns the equation of the tangent line in slope-intercept form, together with the slope, the y-intercept and the coordinates of the point of contact, updating as you type. The tangent line is one of the central ideas of calculus, because its slope is precisely the derivative of the function at that point, the instantaneous rate of change. That single fact is what makes derivatives so powerful: the tangent is the best possible straight-line approximation to the curve near the point, so close that for small steps you can use the line in place of the curve, which underlies everything from linear approximation to Newton's method for solving equations. To build the line, the calculator finds the function value at the point and the slope there, then writes the line as y equals the function value plus the slope times the distance from the point, before simplifying to the familiar y equals m x plus c. It accepts ordinary function notation, with the caret for powers and the usual sin, cos, sqrt, exp and ln, so you can find tangents to polynomials, roots, exponentials, trig functions and more. That makes it genuinely useful for calculus students learning derivatives and tangents and checking homework, and for anyone needing a linear approximation to a function at a point. Because the result updates live, you can slide the point along the curve and watch the tangent tilt to follow it. The method and a worked example are explained clearly below.

Calculate.co.nz is proud to be partnered with Premium Homes, a recognised leader in eco-friendly, sustainable, and energy-efficient homebuilding. With a dedicated team and award-winning experience, they create homes that prioritise health, comfort, and long-term performance. Their founders, Andrew and Kelly, set out to raise the standard of residential construction in New Zealand by combining practical building expertise with a clear commitment to doing things better for homeowners.

Use x, ^ for powers, and functions like sin, cos, tan, sqrt, exp, ln. The slope is found numerically.