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Gradient calculator (multivariable)

Compute the gradient ∇f = ⟨∂f/∂x, ∂f/∂y, …⟩ of a scalar function of several variables. List your variables, and the tool returns each partial derivative symbolically, the gradient vector in closed form, and ∇f evaluated at an optional point — the direction of steepest ascent.

Related tools

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Gradient calculator (multivariable) is free to use as often as you like, directly from this page. It sits under Calculus in our catalogue, alongside Antilog Calculator (inverse logarithm) and Average rate of change calculator.

How to use it

  1. Open the tool — no signup or install needed.
  2. Enter your input or adjust the available options.
  3. Get your result instantly, then copy or download it.

Frequently asked questions

What does Gradient calculator (multivariable) do?

Compute the gradient ∇f = ⟨∂f/∂x, ∂f/∂y, …⟩ of a scalar function of several variables. List your variables, and the tool returns each partial derivative symbolically, the gradient vector in closed form, and ∇f evaluated at an optional point — the direction of steepest ascent.

What does a concrete case look like?

f = x² + y² → ∇f = (2x, 2y) ; (1, 2) → (2, 4) — the tool shows every step in between, not just the final figure.

When would I actually use this?

Checking a derivative or an integral you worked out by hand, finding where a function turns, and getting a numeric answer when no closed form exists.

What is the most common mistake?

Integrating across a discontinuity as if it were not there. A numeric method will happily return a finite value for an integral that diverges — check the domain before trusting the number.

What else is filed next to it?

Antilog Calculator (inverse logarithm), Average rate of change calculator and Bernoulli ODE Solver share its section. They are not variants of it — being filed together is not the same as being alike — but that is where to look if this turned out not to be the tool you wanted.

Where do the figures come from?

Symbolic results are exact; numeric ones come from adaptive quadrature or a standard step method, and the tool reports which. Where both are available, compare them — a large gap means the problem is ill-conditioned.

Further reading

All guides →
ExplainerThe Flat Pattern of a Cone Is a Sector, Not a CircleRoll a 50 mm cone 80 mm tall and its pattern is a 190.8° slice of a 94 mm circle. Flatten a nearly cylindrical lampshade and the pattern radius runs to 839 mm — the shallower the taper, the further away the apex.ExplainerA 1 % Drop Rate Does Not Mean One Hundred RunsAt 1 %, a hundred attempts give you 63.4 % — not certainty. Ninety per cent takes 230 attempts and ninety-nine takes 459, and more than a third of players are still empty-handed at a hundred.ExplainerFibonacci and the Golden RatioThe Fibonacci sequence adds each pair of terms to make the next; the ratio of neighboring terms homes in on the golden ratio φ ≈ 1.618. See how, and where the pattern turns up.ExplainerWhat Is a Z-Score? Standard Deviations Above the MeanA z-score is z = (x − μ) / σ — how many standard deviations a value sits from the mean. Learn how to compute it, read the standard normal curve, and turn it into a percentile.How-toHow to Find the Distance Between Two PointsUse the distance formula d = √((x₂−x₁)² + (y₂−y₁)²) to measure the straight-line distance between two points on a plane, with a worked example and the midpoint too.How-toHow to Calculate the Slope of a Line: Rise Over RunFind the slope of a line from two points with m = (y₂ − y₁) / (x₂ − x₁), and read what a positive, negative, zero, or undefined slope tells you.