Gradient Calculator

Use our free gradient calculator to compute the gradient vector ∇f, its magnitude, and directional derivatives for functions of up to three variables.

Math

Mode

f(x, y, z) =

x value

y value

z value

Direction x-component

Direction y-component

Direction z-component

Formula

Compute the gradient vector at any point using numerical central differences. Supports 2D (x,y) and 3D (x,y,z) functions, plus directional derivatives along any vector.

∇f = (∂f/∂x, ∂f/∂y, ∂f/∂z), ||∇f|| = √((∂f/∂x)² + (∂f/∂y)² + (∂f/∂z)²)

Percentage: The percentage value you want to apply

Number: The original number or value

Result: The calculated result

How It Works

1Enter f(x,y,z) using x, y, z variables.
2Enter the evaluation point.
3Select 2D gradient, 3D gradient, or directional derivative.
4For directional, enter the direction vector components.
5Click Calculate.

Examples

∇f for f=x²+y²+z² at (1,2,3)

1.∇f = (2x, 2y, 2z)
2.∇f(1,2,3) = (2, 4, 6)

Result: 7.483314774

Directional derivative of x²+y² along (1,1)

1.∇f = (2, 2)
2.Direction (1,1): unit = (1/√2, 1/√2)
3.D_𝐮 f = 2√2 ≈ 2.828

Result: 2.8284271247

Frequently Asked Questions

The vector of all partial derivatives, pointing in the direction of steepest ascent.

The rate of change of f along a given direction vector 𝐮.

x, y, z — use only x,y for 2D.

Using central difference numerical partial derivatives (h=1e-6).

The length of the gradient vector, indicating the rate of steepest ascent.

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CalculateMe Team

Last updated: 2026-07-15

Frequently Asked Questions

The vector of all partial derivatives, pointing in the direction of steepest ascent.

The rate of change of f along a given direction vector 𝐮.

x, y, z — use only x,y for 2D.

Using central difference numerical partial derivatives (h=1e-6).

The length of the gradient vector, indicating the rate of steepest ascent.

Gradient Calculator

Formula

How It Works

Examples

∇f for f=x²+y²+z² at (1,2,3)

Directional derivative of x²+y² along (1,1)

Frequently Asked Questions

What is the gradient?

What is a directional derivative?

What variables can I use?

How is it computed?

What is the gradient magnitude?

Related Calculators

Gradient Calculator

Formula

How It Works

Examples

∇f for f=x²+y²+z² at (1,2,3)

Directional derivative of x²+y² along (1,1)

Frequently Asked Questions

What is the gradient?

What is a directional derivative?

What variables can I use?

How is it computed?

What is the gradient magnitude?

Related Calculators