Physics · astronautics

Rocket Equation & Delta-v Budget

Stage it, launch it, see how far it can actually go.
Δv = Iₛₚg₀ ln(m₀/m_f)
2-stage · 8.75 km/s

Stages

up to 4

Payload

Real vehicles

Stack

speed
Velocity
0.00 km/s
Mass

Delta-v budget vs. mission targets

Why a preset can fall short of the mission in its own name. This is ideal delta-v, with one specific impulse per stage — and a first stage is given its sea-level figure, which it keeps all the way up. Most of that burn actually happens in near-vacuum, where the same engine is about 10% better: Falcon 9's first stage is 283 s at the pad and around 311 s in vacuum, worth roughly 360 m/s on its own. Add approximate public masses and a deliberately conservative budget, and the Falcon 9 preset reads about 650 m/s below the 9,400 shown for LEO. The vehicle is fine; the single-Isp model is what is missing the difference.

Vehicle performance
Detail
StagePropellantDry massIspWet massMass ratioΔv
MissionTypical Δv neededThis vehicle
Field notes

Why rockets stage, and what Isp really means

How it works

Exhaust speed times a logarithm

The Tsiolkovsky rocket equation says everything a rocket can ultimately do comes down to two numbers: how fast it throws mass out the back (effective exhaust velocity, ve = Ispg₀), and what fraction of its total mass is propellant (the mass ratio, m₀/mf). Δv = ve·ln(m₀/mf) — and because it's a logarithm, each additional unit of mass ratio buys steadily less delta-v, which is exactly why real rockets are mostly propellant by mass and why staging (throwing away dead structure once it's empty) is so valuable. The launch animation isn't just interpolating between a start and end number — it integrates that same equation over time as propellant actually burns, which is also why the velocity gain visibly accelerates late in each stage's burn: the rocket is lightest, and therefore most responsive to its thrust, right before it runs out of fuel.

Worked example

A Falcon-9-like two-stage rocket carrying a 22,800 kg payload to orbit provides about 8.7 km/s of total delta-v from realistic propellant loads and Isp — close to, but a little under, the roughly 9.4 km/s a real launch actually needs once gravity and drag losses during ascent are included, which this idealised vacuum calculation doesn't model.

Why does staging help so much?

Every kilogram of empty tank and engine a spent stage carries has to be accelerated right along with the fuel that's still burning — dropping that dead structure the moment it's empty means the next stage only has to accelerate what's actually left, which the logarithm in the rocket equation rewards heavily.

What is specific impulse, physically?

Essentially how efficiently an engine converts propellant mass into thrust — a higher Isp means more delta-v from the same propellant mass. Hydrolox engines run high (~450s) because hydrogen's low molecular mass gives very high exhaust velocity; solid rockets run low (~250s) but make up for it with simplicity and enormous thrust.

Why can't ion engines launch a rocket from the ground?

Ion engines have superb Isp (1,500–4,000+ seconds) but famously low thrust — often measured in millinewtons — nowhere near enough to overcome a launch vehicle's own weight at liftoff. They're extraordinary for gradually raising an already-orbiting spacecraft's delta-v over months, not for the seconds-to-minutes, high-thrust demands of getting off a planet.

Why is this delta-v lower than what real launches actually need?

This tool computes the ideal, gravity-free, drag-free delta-v from mass ratios alone — real rockets spend real thrust fighting gravity throughout the whole ascent and pushing through the atmosphere, typically costing an extra 1.5–2 km/s beyond the "just reach orbital velocity" number. The commonly cited ~9.4 km/s LEO figure already has that penalty baked in.

Ideal vacuum delta-v — no gravity or drag losses. Vehicle presets are approximate public figures for illustration, and mission delta-v targets are typical values that vary by trajectory. Not mission-planning data.
Version history · 1 release
  1. v4.092026-08-23Five physics models, 210 checks — and a preset that misses the mission in its own name

Releases in which this page changed, newest last. Derived from the archived copy of every release, not from notes written afterwards — so it reflects what actually shipped. Site-wide passes are left out; they are in the full changelog.