The short answer is: We do not currently have a single, unified "Formula of the Universe."

The formula that physicists are seeking is called the Theory of Everything (TOE). This is a hypothetical, single, coherent theoretical framework that would fully explain and link together all physical aspects of the universe—including matter, energy, space, time, and all fundamental forces.

However, we do have two incredibly powerful, separate mathematical formulas that successfully describe 99.9% of all observable phenomena.

Here is a breakdown of the two dominant formulas we currently use, followed by the leading candidate for the ultimate unified formula.

1. The Formula for the Macrocosm: Gravity and Spacetime

The universe on large scales (planets, galaxies, gravity) is described by Albert Einstein’s General Theory of Relativity (GR).

This theory describes gravity not as a force, but as a curvature of spacetime caused by mass and energy. This is arguably the most famous and powerful single formula in physics, describing the evolution of the cosmos itself.

The Formula (Einstein Field Equations):

$$ G_{\mu\nu} + \Lambda g_{\mu\nu} = \frac{8\pi G}{c^4} T_{\mu\nu} $$

What it means in simple terms:

$$\text{(Curvature of Spacetime)} = \text{Constant} \times \text{(Mass and Energy)}$$

• $G_{\mu\nu}$ and $g_{\mu\nu}$ describe the geometry and curvature of spacetime.
• $T_{\mu\nu}$ (the stress–energy tensor) describes the distribution of all matter and energy in that spacetime.
• $\Lambda$ (Lambda) is the Cosmological Constant, representing Dark Energy, which drives the accelerated expansion of the universe.
• $G$ is the Gravitational Constant, and $c$ is the speed of light.

2. The Formula for the Microcosm: Matter and Forces

The universe on small scales (atoms, particles, and non-gravitational forces) is described by The Standard Model of Particle Physics.

This is not a single equation but a set of equations compiled into a single mathematical structure called the Standard Model Lagrangian($\mathcal{L}$). The Lagrangian is the core mathematical function in physics that allows scientists to calculate how particles interact and move.

The Formula (Standard Model Lagrangian):

$$\mathcal{L}{SM} = \mathcal{L}{\text{Dirac}} + \mathcal{L}{\text{Yang-Mills}} + \mathcal{L}{\text{Higgs}}$$

While the full equation is notoriously complex (it can take up several pages), it successfully describes the:

1. Electromagnetic Force (light, electricity).
2. Weak Nuclear Force (radioactive decay).
3. Strong Nuclear Force (holds atomic nuclei together).
4. All known elementary particles (quarks, leptons, bosons, and the Higgs field).

The Great Conflict: Why We Don't Have a Single Formula

The problem is that General Relativity (the rulebook for the very big) and the Standard Model (the rulebook for the very small) are fundamentally incompatible.

• General Relativity works perfectly for smooth, large-scale structures.
• The Standard Model (Quantum Mechanics) works perfectly for discrete, tiny particles.

When physicists try to combine them mathematically—for instance, to describe conditions at the Big Bang or inside a black hole where matter is infinitely small and dense—the resulting calculations produce nonsense (infinite values). Therefore, we cannot use both formulas simultaneously.

The final "Formula of the Universe" must resolve this conflict.

3. The Leading Candidate for the TOE: String Theory

Currently, the most mathematically robust framework attempting to unify General Relativity and the Standard Model into a single formula is String Theory (and its encompassing version, M-Theory).

The Core Idea:

String Theory posits that all elementary particles (like quarks and electrons) are not zero-dimensional points, but rather tiny, vibrating, one-dimensional "strings." The frequency at which a string vibrates determines the particle it represents (e.g., one vibration frequency might be an electron; another might be a photon).

Crucially, one of the modes of vibration naturally corresponds to the graviton—the hypothetical quantum particle of gravity. In this way, gravity is inherently included alongside the other forces, unifying them all under one mathematical roof.

The Formula (M-Theory Equations):

M-Theory, which incorporates five different superstring theories, is not defined by a single simple equation but by complex mathematical frameworks involving high-level geometry (Calabi-Yau manifolds) and up to 11 dimensions of spacetime.

Because the underlying mathematics is exceptionally complex and still incomplete, there is no single, concise equation to write down for the Theory of Everything, but the goal is to find one comprehensive set of equations whose low-energy limit gives us both General Relativity and the Standard Model.