C3 (Characteristic Energy) Calculator

What It Does

The C3 Calculator computes C3 = v∞² (km²/s²), the characteristic energy of a hyperbolic departure trajectory. Input the hyperbolic excess velocity at Earth departure and the calculator returns C3. It also runs the inverse: given a target body (Mars, Venus, Jupiter, lunar transfer) and a transfer type (Hohmann, fast, ballistic), it returns the required C3 so you can match against published launch vehicle C3-vs-payload curves.

Key Features

• C3 from hyperbolic excess velocity (v∞)
• Inverse: required C3 for Mars, Venus, Jupiter, lunar, NEO transfers
• Comparison against published launch vehicle C3-vs-payload curves
• Support for Hohmann, fast-transfer, and ballistic trajectory types

Why It Matters

C3 is the universal currency of interplanetary launch. Every launch vehicle publishes its payload mass capability as a function of C3 (Falcon Heavy, SLS, Atlas V, Vulcan, Ariane 6 — all of them). Mission designers picking a launch vehicle work in C3, not delta-V, because the vehicle's upper stage performance is what actually delivers the spacecraft to the departure trajectory. Knowing the C3 for a Mars Hohmann transfer (about 9 km²/s²) vs a Jupiter direct (about 80 km²/s²) is the difference between a $100M launch and a $400M launch.

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