What equation does this use?

The Tsiolkovsky rocket equation: Δv = Isp × g0 × ln(m0/mf). We use g0 = 9.80665 m/s² by default.

How are stages handled?

Stages are stacked bottom to top. Each lower stage carries the full mass of all upper stages and payload when it burns. After a stage burns, only its dry mass is carried until staging occurs.

Does this include gravity or aerodynamic losses?

No. This is ideal Δv in a vacuum. Real missions require additional margin for gravity and drag losses.

Yes. All calculations run locally in your browser; nothing is uploaded.

Rocket Delta-V Calculator (Multi-Stage)

Model up to 4 stages with Isp, dry mass, propellant mass, and payload. We’ll compute per-stage and total Δv using the Tsiolkovsky rocket equation—privately, in your browser.

Inputs

Payload mass (kg)

g₀ (m/s²) (standard 9.80665)

Results

Total Δv: –

Per-stage Δv:

–

Notes:

Ideal vacuum Δv only. Real missions need margin for gravity/drag losses and guidance.

What This Calculator Does

We apply the Tsiolkovsky rocket equation per stage. When computing a lower stage, we treat the full stack above (all upper stages at their ignition mass plus payload) as its payload. After a stage burns, only its dry mass is carried until staging occurs; the Δv computation uses the stage’s propellant mass to form the mass ratio. This matches the standard multi-stage idealization used in conceptual design.

FAQs

Do I enter Isp in seconds?

Yes. The calculator converts Isp (s) to m/s using your g₀ value.

Should I include engine mass in dry mass?

Typically yes—dry mass should include everything not propellant for that stage (structure, tanks, engines, avionics).

Can I model staging mass penalties?

For a quick estimate, add any interstage/adapter mass to the dry mass of the relevant stage.

Understanding Rocket Delta-V and the Rocket Equation

When planning any space mission — whether it is launching a satellite into Earth orbit, sending a probe to Mars, or escaping the Solar System — one of the most important calculations engineers perform is the rocket’s delta-V (Δv). Delta-V literally means “change in velocity.” It tells us how much a spacecraft can speed up, slow down, or change direction, and therefore whether it can complete its planned mission profile.

The Tsiolkovsky Rocket Equation

The foundation of delta-V calculations is the Tsiolkovsky rocket equation, named after Russian scientist Konstantin Tsiolkovsky. The equation is:

Δv = Isp × g₀ × ln(m₀ / m_f)

Here, Isp is the engine’s specific impulse (a measure of efficiency, usually expressed in seconds), g₀ is standard gravity (9.80665 m/s²), m₀ is the initial mass of the rocket stage (including fuel, structure, and payload), and m_f is the final mass after the propellant has been burned. The natural logarithm ln(m₀/m_f) captures the fact that only part of the rocket’s starting mass is propellant, and as fuel burns off, the vehicle gets lighter and accelerates faster.

Why Staging Matters

Real rockets are almost never single-stage, because carrying all the dry structure of empty tanks reduces efficiency. Instead, engineers use multi-stage rockets. When a lower stage finishes its burn, it is discarded, leaving the upper stages lighter. Each stage therefore has its own Δv contribution. The total mission Δv is the sum of all the stages. This is why your calculator allows you to enter multiple stages — each with its own Isp, dry mass, and propellant mass — to see how staging strategies affect the final result.

What Delta-V Means in Practice

To put things into perspective:

Reaching Low Earth Orbit (LEO) typically requires about 9.3–10 km/s of delta-V, depending on launch site and trajectory.
Going from LEO to the Moon requires about another 4 km/s.
Sending a spacecraft on a Mars transfer needs around 3.6–4 km/s from LEO.
Escaping Earth entirely for interplanetary or interstellar missions requires more than 11 km/s relative to the planet’s surface.

These values vary slightly by space agency and launch site. NASA, ESA, Roscosmos, ISRO, JAXA, and private companies like SpaceX or Blue Origin all use similar delta-V budgeting methods when planning missions.

Specific Impulse (Isp)

Specific impulse is a key driver of rocket performance. It measures how effectively a rocket engine turns fuel mass into thrust. Chemical engines typically range from 250 to 450 seconds (sea-level vs. vacuum optimized). Advanced electric or ion thrusters used in deep space can achieve several thousand seconds of Isp, but at much lower thrust.

Limitations and Real-World Losses

This calculator shows ideal vacuum delta-V. In reality, rockets must overcome atmospheric drag, steering losses, and the effect of Earth’s gravity while ascending. Engineers therefore add “margins” of several hundred meters per second to ensure the mission succeeds. Still, the rocket equation gives the clean, theoretical baseline that all mission planning starts with.

Why Use This Tool?

A rocket delta-V calculator is valuable for students, hobbyists, engineers, and space enthusiasts. It helps illustrate the tyranny of the rocket equation — the exponential difficulty of carrying enough propellant for ambitious missions. By experimenting with different stage designs, payload masses, and specific impulses, you can see why real space agencies carefully balance efficiency, staging, and technology choice for each mission.

Disclaimer: This tool is for educational purposes only. It demonstrates the ideal rocket equation and should not be used for actual mission-critical planning without professional aerospace engineering review.