About Sigmoid Function Calculator
This sigmoid function calculator plots 1 / (1 + e^-x) and its derivative and evaluates both at any value of x you type. It is free, needs no sign-up and runs in your browser, so nothing you enter is uploaded.
The sigmoid squashes every real number into the range 0 to 1, with 0.5 at x = 0, so it is the natural output for a yes-or-no probability and the basis of logistic regression. Its derivative, sigmoid times one minus sigmoid, is largest at 0 where it equals 0.25 and shrinks quickly: at x = 5 the slope is only about 0.007.
That shrinking slope is the cause of the vanishing gradient problem. In a deep network, gradients pass through one sigmoid per layer and each can cut the signal to a quarter or less, which is why ReLU replaced it in hidden layers. The code here uses a numerically stable form for large negative inputs.
How to use Sigmoid Function Calculator
- Choose a function from the menu, or "Compare all" to overlay the curves.
- For leaky ReLU, ELU and swish, set the extra parameter (alpha or beta) if you want something other than the default.
- Type an x to see f(x) and f'(x), and read the table of values.
- Zoom, pan and trace the plot to read the curve. Double-tap resets the view.
- For softmax, enter your scores separated by commas, set the temperature and read the probabilities and the steps.
- Read the strengths and weaknesses under the plot to compare the functions.
Features
- Nine activation functions with formulas and derivatives rendered in LaTeX.
- Interactive plot of the function and its derivative, with zoom, pan, trace and PNG download.
- A compare view of eight functions on one plot.
- Parameters for leaky ReLU (alpha), ELU (alpha) and swish (beta).
- GELU computed exactly with the error function, not the tanh approximation.
- Softmax with temperature and a worked, numerically stable calculation.
- A value table, range, and plain-language strengths and weaknesses for each function.
Worked examples
x = -4, -2, 0, 2, 4 gives -4: 0.018, -2: 0.1192, 0: 0.5, 2: 0.8808, 4: 0.982
The derivative at x = 2 is 0.105.
Privacy: how it works
- All calculations and plots run in your browser tab. Nothing is sent to Ulkaa or anyone else.
Tips
- Compare the derivative curves: where one is flat near zero, learning is slow in that region of input.
- Try a leaky ReLU with a large alpha such as 0.3 to see how the negative side tilts, and a swish beta of 5 to see it approach ReLU.
- For softmax, add 100 to every score: the probabilities do not change, because only the differences matter.
- Scores with one very large value give a probability close to 1 for that class, whatever the others are.
Frequently asked questions
Is it really free?
Yes. There is no price, no trial and no credit card. Ulkaa Tool does the work with your own device, so there is no server bill to pass on to you.
Do I need an account?
No. There is no sign-up and no login. Open the page and use it. An Ulkaa account is not needed for anything on this tool.
Does it run in my browser?
Yes. Your inputs are processed by code running in your browser tab, on your own device.
Is my data uploaded?
No. Your inputs are never sent to Ulkaa or to anyone else. You can check this yourself by watching the Network tab in your browser developer tools while you use the tool.
What is the range of the sigmoid?
Strictly between 0 and 1. It never reaches either value, but approaches them for large negative and positive inputs.
What is the sigmoid of 0?
Exactly 0.5.
More Activation Function Plotter pages
- Activation Function PlotterPlot any activation function and its derivative, evaluate it at a point, or turn scores into softmax probabilities.
- Tanh Function CalculatorEvaluate tanh and its derivative at any x, and plot both.
- ReLU Activation FunctionPlot max(0, x) and its derivative and evaluate them at any input.
- Leaky ReLU CalculatorSet the negative slope alpha and see how leaky ReLU differs from ReLU.
- ELU Activation FunctionPlot the exponential linear unit and its derivative for any alpha.
- GELU Activation FunctionPlot the Gaussian error linear unit and its derivative, and evaluate it at any x.
- Swish (SiLU) Activation FunctionPlot x times sigmoid(beta x) and its derivative, and change beta.
- Softplus Function CalculatorPlot softplus and its derivative, which is exactly the sigmoid.
- Softmax CalculatorTurn a list of scores into probabilities, with the working shown.