Ideal Rocket Equation Calculator
Free calculate delta-v, specific impulse, initial mass, or final mass using the tsiolkovsky rocket equation.
Input Parameters
Typical: 200-450 s (chemical), 2000-10000 s (ion)
Results
Enter values to calculate
What is the Ideal Rocket Equation?
The ideal rocket equation, also known as the Tsiolkovsky rocket equation, describes the relationship between the velocity change (delta-v) a rocket can achieve and the mass ratio of propellant to total mass.
This fundamental equation in rocketry shows that to achieve higher delta-v, you need either more propellant (higher mass ratio) or a more efficient engine (higher specific impulse). It's the basis for all rocket design and mission planning.
The equation assumes no external forces (gravity, drag) and is ideal for calculating the theoretical maximum velocity change. Real rockets require additional delta-v to overcome gravity and atmospheric drag.
Ideal Rocket Equation Formula
Where:
- • Δv = Delta-v (velocity change) in m/s
- • vₑ = Effective exhaust velocity = Isp × g₀
- • Isp = Specific impulse in seconds
- • g₀ = Standard gravity = 9.80665 m/s²
- • m₀ = Initial mass (with propellant) in kg
- • m_f = Final mass (without propellant) in kg
Rearranged formulas:
Isp = Δv / (g₀ × ln(m₀/m_f))
m₀ = m_f × e^(Δv/(Isp×g₀))
m_f = m₀ / e^(Δv/(Isp×g₀))
How to Calculate
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1
Identify what to solve for
Determine whether you need delta-v, specific impulse, initial mass, or final mass.
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2
Convert masses to kilograms
Ensure all mass values are in the same units (kg) for consistent calculations.
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3
Apply the appropriate formula
Use Δv = Isp×g₀×ln(m₀/m_f) for delta-v, or rearrange to solve for other variables.
Practical Examples
Example 1: Chemical Rocket
A rocket with Isp = 300 s starts with 1000 kg and ends with 200 kg. Calculate delta-v.
Solution:
vₑ = 300 s × 9.80665 m/s² = 2,942 m/s
Δv = 2,942 × ln(1000/200) = 2,942 × ln(5)
Δv = 4,736 m/s ≈ 4.7 km/s
Example 2: Ion Thruster
An ion thruster with Isp = 3000 s needs 5 km/s delta-v. If final mass is 500 kg, what initial mass is needed?
Solution:
vₑ = 3000 × 9.80665 = 29,420 m/s
m₀ = 500 × e^(5000/29420) = 500 × e^0.17
m₀ = 593 kg (93 kg propellant)
Applications
Spacecraft Design
Essential for determining propellant requirements, staging strategies, and mission feasibility.
Mission Planning
Calculating delta-v budgets for orbital maneuvers, interplanetary transfers, and landing missions.
Engine Selection
Comparing different propulsion systems (chemical, ion, nuclear) based on specific impulse requirements.
Education
Teaching fundamental principles of rocket propulsion and orbital mechanics.
Frequently Asked Questions
What is delta-v?
Delta-v (Δv) is the total velocity change a rocket can achieve. It's measured in m/s and represents the "fuel" needed for maneuvers. Earth orbit requires ~9.4 km/s, Mars transfer ~6 km/s.
What is specific impulse (Isp)?
Specific impulse measures engine efficiency - how long 1 kg of propellant can produce 1 N of thrust. Higher Isp means more efficient. Chemical rockets: 200-450 s, ion thrusters: 2000-10000 s.
Why do rockets use staging?
Staging allows discarding empty fuel tanks, reducing final mass. This dramatically increases delta-v. A 2-stage rocket can achieve much higher velocities than a single-stage rocket with the same total mass.
What is the mass ratio?
Mass ratio = m₀/m_f. Higher ratios mean more propellant relative to payload. Typical values: 3-5 for single stage, 10-20+ for multi-stage rockets.
Does this account for gravity and drag?
No, this is the ideal equation assuming no external forces. Real missions require additional delta-v: ~1.5-2 km/s for gravity losses, ~0.3-0.5 km/s for atmospheric drag during launch.