Function Runtime Calculator

Model execution growth using logs powers and exponentials. Review values sample ranges and trend plots. Save outputs for study reports or quick checking later.

Calculator

Runtime model

Input size n

Coefficient a

Overhead c

Repetitions r

Coefficient unit

Polynomial exponent p

Log or exponential base

Graph range start

Graph range end

Graph step

Example Data Table

Example settings: linear model, a = 0.02 ms, c = 0.10 ms, r = 1.

n	g(n)	Runtime (ms)
10	10	0.30
25	25	0.60
50	50	1.10
100	100	2.10

Formula Used

Main runtime formula: T(n) = r × (c + a × g(n))

T(n) is the estimated runtime.
r is the number of repetitions.
c is the fixed overhead per run.
a scales the chosen growth function.
g(n) is the selected runtime model.

Model	g(n)	Complexity
Constant	1	O(1)
Logarithmic	log_b(n)	O(log n)
Linear	n	O(n)
Linearithmic	n · log_b(n)	O(n log n)
Polynomial	n^p	O(n^p)
Quadratic	n²	O(n²)
Cubic	n³	O(n³)
Exponential	bⁿ	O(bⁿ)

How to Use This Calculator

Choose the runtime model that best matches your function.
Enter input size n.
Set coefficient a and overhead c in your preferred unit.
Enter repetitions r for repeated execution.
Use exponent p for polynomial mode.
Use base b for logarithmic or exponential mode.
Set range values for the graph and generated table.
Click Calculate Runtime to show the result above the form.
Review the graph and range table.
Export the current output as CSV or PDF.

FAQs

1. What does this calculator estimate?

It estimates runtime using a chosen growth model, a scaling coefficient, fixed overhead, repetitions, and input size. It helps compare how execution time changes as n grows.

2. Is this an exact stopwatch measurement?

No. It is a mathematical estimate. Real runtime also depends on hardware, memory, language implementation, input structure, and system load.

3. When should I use the polynomial option?

Use polynomial when your runtime follows n raised to a custom power, such as n^1.5, n^2.2, or another measured exponent from analysis.

4. What is the overhead term?

Overhead is the fixed time added to each run. It represents setup cost, constant checks, loading, or any runtime that does not grow with n.

5. Why do logarithmic and exponential models need a base?

The base defines the curve shape. Logarithmic base changes the growth scale. Exponential base changes how rapidly runtime explodes as n increases.

6. Why are large exponential results huge?

Exponential functions grow extremely fast. Even small increases in n can produce massive runtime estimates. That behavior is normal for exponential complexity.

7. What do the unit conversions show?

The calculator converts the final estimate into nanoseconds, microseconds, milliseconds, and seconds. This helps you interpret the same result in practical units.

8. Can I use this for coursework and reports?

Yes. The table, graph, formula section, and export tools make it useful for study notes, algorithm discussions, and runtime comparison writeups.