🚀 What is the Rocket Equation?
The Tsiolkovsky Rocket Equation is the core formula behind modern rocketry. It defines the relationship between a rocket’s change in velocity (Δv), its exhaust velocity, and the mass it carries before and after fuel is burned.
In simple terms:
The more fuel you add, the more fuel you need to carry that fuel.
This creates a logarithmic wall for scaling rockets to the Moon, Mars, or beyond.
📐 The Equation (in Math)
Δv = ve × ln(m₀ / mf)
Where:
- Δv = change in velocity (m/s)
- vₑ = exhaust velocity of the rocket (m/s)
- m₀ = initial mass (rocket + fuel)
- m_f = final mass (rocket without fuel)
🔢 Try It Yourself: Interactive Calculator
We’ve built a simple web-based calculator where you can solve for any variable. Just enter the values you know, choose what to solve for, and let the math show you what’s possible.
👉 Launch the Rocket Equation Calculator (opens in a new tab)
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🧠 Why We Made This
There are a lot of wild claims flying around right now — especially from billionaires hyping up rockets, Mars colonies, and 100-ton payloads to the Moon. But physics doesn’t care about hype.
As Carl Sagan famously said:
“Extraordinary claims require extraordinary evidence.”
This calculator helps expose those claims for what they are — or aren’t.
We’re building this site to educate, simplify, and ground space discussions in reality. The Rocket Equation isn’t a meme. It’s a hard limit.
🚫 The Starship Illusion: Why It Can’t Go to Mars (Or Even Orbit Properly)
Let’s talk about Starship, the rocket Elon Musk claims will take people to Mars.
🔻 The Reality:
- Fastest Starship has ever gone: ~7.3 km/s
- Speed required just to stay in Earth orbit: ~7.8 km/s
- Speed needed for trans-lunar injection: ~11.2 km/s
- Speed for Mars transfer: ~15+ km/s (depending on trajectory and payload)
It’s never even hit orbital velocity — and that’s with no cargo, no crew, and no successful reentry.
And unlike Saturn V, whose theoretical delta-v was well above what was actually achieved, Starship’s best-case numbers still fall short of what’s needed for the Moon — even under ideal, stripped-down, cargo-free conditions.
🚀 Why They “Need” So Many Ships
Elon now claims we’ll need 20–30 separate Starships just to refuel one trip to the Moon or Mars.
That’s not efficiency — that’s desperation.
Originally, Starship wasn’t even meant to leave Earth with humans on board. NASA’s own Artemis documents showed it would be used only as a lunar elevator — a lander to shuttle humans between lunar orbit and the lunar surface.
But now they act like it’ll go Texas to Mars in one shot.
It won’t. It can’t. There isn’t enough energy in the chemical bonds of the fuel to do so.
📉 The Mars Myth, Busted
Even using Elon’s most optimistic specs:
- Starship doesn’t have the Δv to go from Earth to Mars fully loaded
- Refueling in orbit would require dozens of complex, unproven dockings
- It still can’t survive reentry reliably — every attempt has failed or disintegrated
🍌 It Can’t Even Launch a Banana
Let’s be blunt: Starship can’t even get a banana to space.
And yes — they literally tried. It crashed in the Indian Ocean.
🧠 Why This Calculator Exists
This is why we made the Rocket Equation Calculator:
To translate hype into hard numbers.
Because a logarithmic fuel curve doesn’t care about your TED Talk or your crypto fortune.
Physics wins. Every time.