Ideal Rocket Equation Calculator
Calculate rocket delta-v from exhaust velocity, initial mass, and final mass using the Tsiolkovsky equation.
What Is the Ideal Rocket Equation?
The Tsiolkovsky rocket equation links how much speed a rocket gains to its exhaust velocity and how much mass it sheds as propellant. Aerospace engineers, Kerbal Space Program players, and mission planners use it to estimate delta-v budgets before detailed trajectory design.
The Tsiolkovsky Formula
For a rocket that expels mass at constant exhaust velocity:
$$\Delta v = v_e \ln\left(\frac{m_0}{m_f}\right)$$Here \(v_e\) is effective exhaust velocity in m/s, \(m_0\) is initial mass including propellant, and \(m_f\) is final mass after burn. The natural logarithm of the mass ratio sets how much velocity change is possible.
Mass Ratio and Propellant
Mass ratio \(m_0/m_f\) must exceed 1. A 10,000 kg rocket that ends at 2,000 kg has ratio 5 and burns 8,000 kg of propellant. Higher exhaust velocity or a larger mass ratio both increase delta-v.
Related tools: Ideal Gas Law Calculator and Drone Flight Time Calculator.
Frequently Asked Questions
What is delta-v?
Delta-v is the change in velocity a rocket can achieve from propulsion alone, ignoring gravity and drag. Mission planners stack delta-v requirements for each maneuver.
Why must final mass be less than initial mass?
The rocket must burn propellant to accelerate. If final mass equals or exceeds initial mass, the mass ratio is 1 or less and ln(m₀/m_f) is zero or undefined.
What is a typical exhaust velocity?
Chemical rockets often have effective exhaust velocities around 3,000 to 4,500 m/s. Ion thrusters can exceed 30,000 m/s but produce much lower thrust.
Does this include gravity losses?
No. This is the ideal rocket equation in vacuum with no external forces. Real launches need extra delta-v to fight gravity and atmospheric drag.
How do I convert specific impulse to exhaust velocity?
Multiply specific impulse in seconds by standard gravity (about 9.81 m/s²). For example, Isp of 300 s gives vₑ near 2,940 m/s.
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