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Live now · 150,114 equations · 1,000 domains

From intuition
to abstraction

Every formula hides an image. Explore 150,114 equations through animation, sound, simulation, mathematical art, and real-world stories.

A living museum where rigor meets cinematic clarity — not dead symbols on a page.

Explore equationsVisual studioGenerate art

Interactive studios — all connected

Visual Studio

Explore, tweak parameters, export — end to end.

Sound Studio

Explore, tweak parameters, export — end to end.

Art Engine

Explore, tweak parameters, export — end to end.

Calculators

Explore, tweak parameters, export — end to end.

What we offer

Not just a database — a visual studio for mathematics

Rigor meets cinematic clarity. Explore, animate, and share equations the way they deserve to be understood.

From intuition to abstraction

Visualize

Interactive graphs, Manim-style animations, and real-world photo overlays — every formula hides an image waiting to be revealed.

Explore

Serialized learning arcs

Story mode

Follow curated paths from Newton to quantum AI. Metaphor-first narratives, formal derivations, and connections across domains.

Explore

Equations as living artifacts

Share & create

Generate mathematical art, hear equations as sound, and export cinematic share cards with real-world impact stories.

Explore
Start exploringView galleryShare cards
Visual portfolio

Every formula hides an image

Hover to preview — animated scenes, real-world photos, and living mathematics. Inspired by cinematic math communication.

Full collection

Equation of the Day

Formal Sciences
Beginner

Pythagorean Theorem

In a right triangle, the square of the hypotenuse equals the sum of squares of the other two sides.

Why it matters

How do we measure distance when paths turn at right angles?

Explore today's equationPlay its sound
a2+b2=c2a^2 + b^2 = c^2

Our philosophy

We're not just building a reference library.
We're not just making animations.
We combine mathematical rigor with visual clarity
— so every learner can move from intuition to abstraction.

Like the best science communicators, we start with metaphor, build to formal math, and leave you with wonder — plus shareable artifacts you can take anywhere.

Explore the universeOur story
For everyone

Built for curious minds at every stage

Whether you're cramming for finals, designing rockets, or teaching the next generation — equations should feel alive.

For Students

Finally understand the equations on your exam — and why they matter.

  • Story mode for every major formula
  • Interactive graphs & sound
  • Learning paths by topic
Learn more

For Engineers

From Navier-Stokes to rocket equations — see the math behind the machines you build.

  • Rocket & fluid simulations
  • Real-world applications
  • Shareable equation cards
Learn more

For Teachers

Turn your classroom into an equation planetarium.

  • Cinematic timeline & story mode
  • Visual demos for lectures
  • Classroom use-case guide
Learn more

For Researchers

Navigate 150,114 equations across 1,000 domains — connected by a living knowledge graph.

  • Universe map connections
  • Frontier science paths
  • Deep derivation summaries
Learn more
Launch collection

25 polished equation experiences

Full story mode, interactive visuals, sound, and shareable cards — curated for public launch.

Browse all
Featured pick

Pythagorean Theorem

Beginner
a2+b2=c2a^2 + b^2 = c^2

In a right triangle, the square of the hypotenuse equals the sum of squares of the other two sides.

Formal Sciences
Mathematics
View

Equation Universe

Pythagorean Theorem

a2+b2=c2a^2 + b^2 = c^2

Real-world impact

Architecture & GPS triangulation

Right-triangle geometry anchors surveying, construction, and navigation.

Photo: Unsplash — skyscrapers

In a right triangle, the square of the hypotenuse equals the sum of squares of the other two sides.

equation-universe.vercel.app

Post
Polished
Polished

Taylor Series

Intermediate
f(x)=∑n=0∞f(n)(a)n!(x−a)nf(x) = \sum_{n=0}^{\infty} \frac{f^{(n)}(a)}{n!}(x-a)^n
Formal Sciences
View
Polished

Fourier Transform

Advanced
f^(ξ)=∫−∞∞f(x) e−2πixξ dx\hat{f}(\xi) = \int_{-\infty}^{\infty} f(x)\, e^{-2\pi i x \xi}\, dx
Formal Sciences
View
Polished

Bayes' Theorem

Intermediate
P(A∣B)=P(B∣A) P(A)P(B)P(A|B) = \frac{P(B|A)\, P(A)}{P(B)}
Formal Sciences
View
Polished
Polished
Polished

Bernoulli Equation

Intermediate
P+12ρv2+ρgh=constantP + \frac{1}{2}\rho v^2 + \rho g h = \text{constant}
Physical Sciences
View
Polished

Navier-Stokes Equation

Research
ρ(∂v∂t+v⋅∇v)=−∇P+μ∇2v+f\rho\left(\frac{\partial \mathbf{v}}{\partial t} + \mathbf{v}\cdot\nabla\mathbf{v}\right) = -\nabla P + \mu\nabla^2\mathbf{v} + \mathbf{f}
Physical Sciences
View
Polished

Wave Equation

Intermediate
∂2u∂t2=c2∂2u∂x2\frac{\partial^2 u}{\partial t^2} = c^2 \frac{\partial^2 u}{\partial x^2}
Physical Sciences
View
Polished

Heat Equation

Intermediate
∂u∂t=α∇2u\frac{\partial u}{\partial t} = \alpha \nabla^2 u
Physical Sciences
View
Polished
Polished

Entropy Equation

Advanced
ΔS=∫δQrevT\Delta S = \int \frac{\delta Q_{\text{rev}}}{T}
Physical Sciences
View
Polished

Maxwell's Equations

Advanced
∇⋅E=ρε0,∇×E=−∂B∂t\nabla \cdot \mathbf{E} = \frac{\rho}{\varepsilon_0}, \quad \nabla \times \mathbf{E} = -\frac{\partial \mathbf{B}}{\partial t}
Physical Sciences
View
Polished

Lorentz Force

Advanced
F=q(E+v×B)\mathbf{F} = q(\mathbf{E} + \mathbf{v} \times \mathbf{B})
Physical Sciences
View
Polished
Polished

Schrödinger Equation

Advanced
iℏ∂ψ∂t=H^ψi\hbar \frac{\partial \psi}{\partial t} = \hat{H}\psi
Physical Sciences
View
Polished
Polished
Polished

Shannon Entropy

Intermediate
H=−∑ipilog⁡2piH = -\sum_{i} p_i \log_2 p_i
Formal Sciences
View
Polished

SIR Model

Intermediate
dSdt=−βSI,dIdt=βSI−γI,dRdt=γI\frac{dS}{dt} = -\beta SI, \quad \frac{dI}{dt} = \beta SI - \gamma I, \quad \frac{dR}{dt} = \gamma I
Medical Sciences
View
Polished

Logistic Growth Equation

Intermediate
dNdt=rN(1−NK)\frac{dN}{dt} = rN\left(1 - \frac{N}{K}\right)
Biological Sciences
View
Polished
Polished

Gradient Descent Update Rule

Intermediate
θt+1=θt−η∇θL(θt)\theta_{t+1} = \theta_t - \eta \nabla_\theta L(\theta_t)
Information Sciences
View
Polished

Transformer Attention

Advanced
Attention(Q,K,V)=softmax(QKTdk)V\text{Attention}(Q,K,V) = \text{softmax}\left(\frac{QK^T}{\sqrt{d_k}}\right)V
Information Sciences
View
Premium paths

5 flagship learning journeys

Deep, curated paths with story-enriched equations — serialized arcs from intuition to abstraction.

All paths

Equations That Changed Civilization

PremiumBeginner

The formulas that redirected human history — from geometry to relativity.

5 equations~6h

Not started — progress saved in your browser

Start path

Physics From Newton to Einstein

PremiumIntermediate

Classical mechanics through spacetime and energy.

5 equations~10h

Not started — progress saved in your browser

Start path

Quantum Reality

PremiumAdvanced

The equations of the subatomic world.

4 equations~12h

Not started — progress saved in your browser

Start path

Rocket Science and Spaceflight

PremiumIntermediate

From Tsiolkovsky to orbital mechanics and cosmology.

5 equations~7h

Not started — progress saved in your browser

Start path

AI and Information Theory

PremiumAdvanced

Entropy, optimization, and the math behind intelligence.

5 equations~10h

Not started — progress saved in your browser

Start path
The Universe Map

Every equation, one connected map

Explore equations, domains, scientists, and real-world applications in an interactive force-directed graph. Start with landmark nodes for a guided tour, or open the full network when you want the complete picture.

Open the Universe Map
Knowledge map

1,000 domains of knowledge

Navigate science like a universe — 13 foundation domains plus 987 specialized fields.

Formal Sciences

formal-sciences

Logic, mathematics, statistics, and the formal structures of knowledge.

5 branches160 equations

Physical Sciences

physical-sciences

The fundamental laws governing matter, energy, space, and time.

9 branches171 equations

Chemical Sciences

chemical-sciences

Reactions, bonds, and the molecular architecture of matter.

6 branches158 equations

Biological Sciences

biological-sciences

Life from molecules to ecosystems, evolution, and neuroscience.

5 branches157 equations

Earth System Sciences

earth-system-sciences

Geology, oceans, atmosphere, and climate dynamics.

5 branches156 equations

Space Sciences

space-sciences

Astronomy, astrophysics, cosmology, and orbital mechanics.

5 branches157 equations

Engineering Sciences

engineering-sciences

Applied science for building machines, structures, and systems.

10 branches161 equations

Medical Sciences

medical-sciences

Human health, disease, pharmacology, and clinical science.

3 branches156 equations

Agricultural Sciences

agricultural-sciences

Food systems, soil, crops, and sustainable agriculture.

2 branches160 equations

Social Sciences

social-sciences

Economics, society, behavior, and human systems.

3 branches161 equations

Information Sciences

information-sciences

Computation, data, AI, and digital systems.

4 branches156 equations

Interdisciplinary Sciences

interdisciplinary-sciences

Cross-domain science bridging multiple fields.

3 branches155 equations

Frontier Sciences

frontier-sciences

Emerging research at the edge of human knowledge.

5 branches156 equations
Browse all 1,000 domains

Equation explainers

SEO-friendly deep dives — each article links to interactive equation experiences.

All articles

Friedmann Equation Explained

How the expansion rate of the universe links matter density, spatial curvature, and dark energy.

10 min read

Pythagorean Theorem Explained

Why a² + b² = c² is the oldest equation still taught to every student — and how it built architecture, navigation, and GPS.

6 min read

Euler's Identity: The Most Beautiful Equation

e^(iπ) + 1 = 0 links five fundamental constants in one line — and powers all of modern signal processing.

7 min read

Taylor Series Explained

How smooth functions become infinite polynomials — and why calculators can compute sin, cos, and e^x.

8 min read

Our mission

We believe equations are the most beautiful language humanity has ever written.

Equation Universe started with a simple frustration: the equations that built civilization are taught like dead symbols on a page. Students memorize. Engineers look up formulas. Teachers lack tools that inspire wonder.

We set out to build something different — a living museum where you can see a Fourier transform ripple, hear a rocket equation climb in pitch, and feel why E = mc² changed the world.

Inspired by mathematical art, NASA-grade science communication, and the clarity of 3Blue1Brown — we're building the platform we wished existed when we were learning.

“Every student deserves an ‘I finally understand this’ moment — not just for homework, but for life.”

— The Equation Universe team

1M+

Equations

1,000

Domains

∞

Wonder

Launch pricing — limited early access

Learn equations like a planetarium, not a textbook

Free to explore today. Join the waitlist for Pro features, classroom tools, and founding-member pricing.

Explorer

Free

forever

Explore the full equation universe — visual, sound, and story.

  • 1M+ equations
  • 1,000 domains
  • Visual & Sound Studio
  • Math Art Gallery
  • Learning paths
Start exploring
Most popular

Pro

Early access

founding member pricing

Premium paths, classroom tools, and launch-day perks for early believers.

  • Everything in Explorer
  • 5 premium learning paths
  • Classroom-ready exports
  • Priority new features
  • Founding member badge
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Institutions

Contact

schools & teams

Volume licensing for classrooms, labs, and engineering teams.

  • Teacher dashboard (coming)
  • SSO & admin controls
  • Custom learning paths
  • Dedicated support
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Equation Universe newsletter

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What if equations could be seen, heard, and felt?

Equation Universe is a living museum — not a textbook. Every formula is a pattern waiting to be explored.

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Mathematical Art Gallery

Polar roses, Lissajous curves, fractals, and chaotic attractors — original art generated from pure mathematics.

Enter the gallery
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Sound Studio

Map equation outputs to frequency, amplitude, and waveform. Hear the shape of mathematics — only after you press play.

Open Sound Studio
Explore

Civilization Timeline

Journey through 14 eras — from Babylonian geometry to the AI age.

Explore timeline
Explore

Universe Map

A force-directed knowledge graph connecting equations across domains, eras, and applications.

Navigate the map
Explore

Learning Paths

15 curated journeys — from Newton to quantum AI, rocket science to mathematical art.

Start a path

Enter the equation planetarium

A hundred thousand equations. One living universe. Start exploring today.

Explore EquationsGenerate Mathematical Art