| Index | Mathematical Formula | Approximate Growth Rate | | :--- | :--- | :--- | | $f_0(n)$ | $n+1$ | Addition | | $f_1(n)$ | $2n$ | Multiplication | | $f_2(n)$ | $2^n \cdot n$ | Exponential | | $f_3(n)$ | ≥ $2↑↑n$ | Tetration (Power Towers) | | $f_m(n)$ | ≥ $2↑^m-1n$ | Hyperoperation |
It is a reminder that even within the cold, hard bounds of finite computation, we can reach toward the infinite. Whether you are a googologist chasing the next record-holding number, a logician mapping the terrain of proof strength, or simply a curious mind wondering what comes after a trillion, the FGH calculator is your compass. fast growing hierarchy calculator
Before we touch the calculator, we must understand the engine. The Fast Growing Hierarchy is a family of functions indexed by ordinal numbers. In layman's terms, think of it as a ladder where each rung is a function that grows faster than all the rungs below it. | Index | Mathematical Formula | Approximate Growth
is typically a specialized tool—often found in "googology" (the study of large numbers) communities—designed to evaluate or simulate these functions, which quickly outpace standard scientific notation. How the Hierarchy Works The hierarchy is a family of functions, f sub alpha The Fast Growing Hierarchy is a family of
As you can see, these functions grow extremely rapidly. Even for small inputs, the values of $f_i(n)$ can become enormous.
Different definitions yield different results. You must choose: