Cosmic Formula Playground & Sandbox
✨ 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
Rotate Explore Understand! ⤵
Cube V = s3 Volume = side × side × side
💡 A cube is a box with equal sides. Its volume tells us how much space it can hold!
Volume V: 125.0 cm³
1 cm 10 cm
🔄 Drag canvas to tilt & spin shape in 3D

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.

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Syllabus

Follow a structured learning path from simple shapes to complex solids.

📖 12 topics
→
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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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Trusted by learners everywhere

A growing community of curious minds exploring math in a more visual and joyful way.

🎓
50K+Learners
📖
30+Formulas
⭐
100+Practice Questions
👥
4.9/5User Rating
STRUCTURED CURRICULUM

Public Learning Path & Syllabus

Follow a logical educational journey through 25 verified physical laws of the cosmos.

✨ Library  ·  Explore  ·  Learn  ·  Understand

Explore 3D formulas
with visuals and real context.

Search, browse, and discover space formulas with interactive visuals, simple explanations, and real-world examples.

All Formulas ✨

120+ formulas with interactive visuals, explanations, and real-world applications.

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Recently Viewed

Continue where you left off.

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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
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Level 3 Space Explorer
12 / 20 XP
✓ 18 Correct
✕ 4 Needs Practice
🔥 5 Day Streak
☀️ 68% Accuracy
🧊 Question 4 of 10
⭐ 60 XP Easy

What is the volume of this sphere?

Use the formula V = 4/3πr3 and π ≈ 3.14.

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Stage Preview Sphere World
Stage 2
Spheres in Real Life

Explore how spheres appear in the real world, from planets to sports balls, and calculate their volume!

💡 Need a Hint?
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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! ›
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Speed Solve 10 questions · 5 minutes
⭐ 50 XP
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Mixed Shapes 10 questions · 8 minutes
⭐ 75 XP
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Real World Objects 8 questions · 6 minutes
⭐ 75 XP
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Challenge Mode 12 questions · 10 minutes
⭐ 100 XP
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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
👥
Trusted by learners everywhere

A growing community of curious minds exploring math in a more visual and joyful way.

🎓
50K+Learners
📖
30+Formulas
⭐
100+Practice Questions
👥
4.9/5User Rating
⚙️ 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
\( V = \frac{4}{3}\pi r^3 \)
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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
→ Hubble expansion
→ Peculiar motion
Time: 0.0 → 13.8 Gyr

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.

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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.

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Galaxies follow the expansion, but gravity still has a say!

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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.

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Keep exploring

Try related labs and topics to deepen your understanding.