Syllabus
Follow a structured learning path from simple shapes to complex solids.
📖 12 topics
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✨ Visual · Interactive · ELI5 · For curious minds
Learn space formulas
visually, not just by heart.
Interactive astronomy, physics & 3D space formulas for curious minds. Cosmic Formula Playground helps you understand 3D shapes, measurements, and physical laws through tactile simulations.
Beginner friendly
Interactive 3D visuals
Learn by doing
Free to explore
💡
A cube is a box with equal sides. Its volume tells us how much space it can hold!
Popular Formulas ✨
Start with a shape and see the formula come to life with interactive visuals.
Explore Cosmic Formulas 🚀
Everything you need to master space and physics formulas, all in one playground.
Library
Explore all formulas with beautiful visuals, examples, and real-world applications.
📖 30+ formulas
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Practice
Test your understanding with fun questions, hints, and step-by-step solutions.
⭐ 100+ questions
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Live Labs
Interact with 3D shapes, change values in real time, and see formulas come to life.
🧪 3D interactive
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STRUCTURED CURRICULUM
Public Learning Path & Syllabus
Follow a logical educational journey through 25 verified physical laws of the cosmos.
All Formulas ✨
120+ formulas with interactive visuals, explanations, and real-world applications.
Recently Viewed
Continue where you left off.
Saved Formulas
Your bookmarked favorites.
✨ Practice · Solve · Build Confidence · Level Up
Practice space formulas
with fun challenges.
Solve interactive questions, get instant feedback, and level up your skills with engaging missions. Turn practice into progress!
Practice Solve Improve!
Your Progress
Level 3
Space Explorer
12 / 20 XP
18 Correct
4 Needs Practice
5 Day Streak
68% Accuracy
🧊
Question 4 of 10
What is the volume of this sphere?
Use the formula V = 4/3πr3 and π ≈ 3.14.
Timed Mission Challenges
Put your skills to the test with quick, focused challenges. Earn XP and keep your streak going!
🔥
5 Day Streak Keep it up!
›
Speed Solve
10 questions · 5 minutes
⭐ 50 XP
Mixed Shapes
10 questions · 8 minutes
⭐ 75 XP
Real World Objects
8 questions · 6 minutes
⭐ 75 XP
Challenge Mode
12 questions · 10 minutes
⭐ 100 XP
Equation Blocks
Drag and use these equation blocks while you practice.
V = s3
Cube Volume
V = l × w × h
Cuboid Volume
V = 4/3πr3
Sphere Volume
V = πr2h
Cylinder Volume
V = 1/3πr2h
Cone Volume
V = 1/3Bh
Pyramid Volume
⚙️ Interactive Parameter Workbench · Pure Math & Real Physics
Formula Sandbox Workbench
Manipulate core space, physics, and geometry variables in real time. Adjust sliders to observe instantaneous recalculations, dimensional derivations, and test real-world astronomical presets.
Geometry
Volume of a Sphere
Preset Scenarios:
COMPUTED RESULT
4.189
m³
\( V = \frac{4}{3}\pi r^3 \)
Step-by-Step Substitution
🧪 Live Lab · Galaxies · Cosmology · For curious minds
LAB 01
Hubble flow & peculiar velocity Hubble Flow & Peculiar Velocity
Explore how the expanding universe and local gravitational tugs combine to shape the velocities we observe in galaxies.
Interactive simulation
Adjust parameters
Real-world examples
Free to explore
Hubble Flow
→ vH = H0 d
Peculiar Velocity
→ vpec
What We Measure
cz = vH + vpec
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Hubble expansion
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Peculiar motion
Build the equation, see it in action ✨
Adjust the sliders below to explore how the Hubble flow and peculiar velocity combine to give the velocity we measure.
The big picture (ELI5) ✨
The universe is expanding, so galaxies farther away move away from us — like dots on a balloon getting farther apart. But galaxies also feel gravity from nearby matter, which can pull them off their smooth expansion. We observe a mix of both effects: the Hubble flow plus a peculiar velocity.
💡
Galaxies follow the expansion, but gravity still has a say!
Worked example
A galaxy is 100 Mpc away with a peculiar velocity of −500 km/s.
Hubble flow:
vH = H0 d = 70 × 100 = 7,000 km/s
Peculiar velocity:
vpec = −500 km/s (toward us)
Observed velocity:
cz = vH + vpec = 7,000 − 500 = 6,500 km/s
✓
So we measure cz = 6,500 km/s, which is smaller than the Hubble flow alone due to the local tug.
Keep exploring
Try related labs and topics to deepen your understanding.