Gradient Of A Function Calculator
Work out gradient of a function instantly with clear inputs, formula shown and shareable results.
About Gradient Of A Function Calculator
The gradient collects the partial derivatives into a vector that points in the direction of steepest increase. Its magnitude is the maximum rate of change, and it is always perpendicular to the level surfaces.
Formula
Gradient
∇f = (∂f/∂x, ∂f/∂y, ∂f/∂z), |∇f| is the maximum rate of change
Worked example
With the default values below, Gradient Of A Function Calculator returns Magnitude of the gradient of 13.00000000. Change any input above and every figure here is recalculated in your browser.
Inputs used
- ∂f/∂x
- 3
- ∂f/∂y
- 4
- ∂f/∂z
- 12
Results
- Magnitude of the gradient
- 13.00000000
- Gradient vector
- (3, 4, 12)
- Unit direction of steepest ascent
- (0.230769, 0.307692, 0.923077)
- Unit direction of steepest descent
- (-0.230769, -0.307692, -0.923077)
Step by step
- 1Values used
- 2Gradient
- 3Magnitude of the gradient= 13.00000000
- 4Gradient vector= (3, 4, 12)
- 5Unit direction of steepest ascent= (0.230769, 0.307692, 0.923077)
- 6Unit direction of steepest descent= (-0.230769, -0.307692, -0.923077)
Assumptions and limits
- The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
- In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
- Figures are rounded for display to 8 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.
How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.
Frequently Asked Questions
For partials 3, 4 and 12?
The magnitude is 13, and the unit direction is (3/13, 4/13, 12/13).
Why does gradient descent use the negative?
Because minimising means moving against the direction of steepest increase, which is the fastest way downhill.