Arc Length Calculator
Calculate the arc length of a curve using calculus
About this calculator
The Arc Length Calculator computes the precise length of a curve between two points using advanced calculus methods. This tool applies the arc length formula, which integrates the square root of 1 plus the derivative squared over a specified interval. It's essential for engineers, mathematicians, and students working with curved paths, road design, cable installations, or any application requiring accurate distance measurements along non-linear trajectories.
How to use
Enter your function f(x) in the input field, then specify the lower and upper bounds of the interval where you want to calculate the arc length. The calculator will automatically compute the derivative, apply the arc length formula, and perform the integration to give you the exact length of the curve.
Frequently asked questions
What is the arc length formula?
The arc length formula is L = ∫[a,b] √(1 + (f'(x))²) dx, where f'(x) is the derivative of your function over interval [a,b].
Can this calculator handle complex functions?
Yes, the calculator can process polynomial, trigonometric, exponential, and logarithmic functions, automatically computing derivatives and performing numerical integration as needed.
What units does the arc length result use?
The arc length result uses the same units as your input coordinates. If your function uses meters, the result is in meters.