ConverterHub

Staging Delta-V Calculator

Enter each stage's Isp and wet/dry mass to find total delta-v.

How it is calculated

Each stage's velocity change comes from the Tsiolkovsky rocket equation: Δv = Isp × g0 × ln(mwet ÷ mdry), with Isp in seconds, g0 = 9.80665 m/s² and masses in any one consistent unit (kg, tonnes or pounds). The tool computes this for stage 1 and stage 2 separately and adds them: Δvtotal = Δv1 + Δv2, all in m/s rounded to one decimal. For each stage, wet mass must exceed dry mass, dry mass must be above zero and Isp positive, otherwise nothing is returned. The tool treats the stages independently, so for stage 1 the wet and dry masses must include everything above it, including the whole second stage and payload.

Worked example

Stage 1: Isp 280 s, wet 500,000 kg, dry 150,000 kg. That dry figure includes the full second stage (120,000 kg) plus 30,000 kg of empty first stage. ln(500,000 ÷ 150,000) = ln(3.333) = 1.204, so Δv1 = 280 × 9.80665 × 1.204 = 3,305.9 m/s. Stage 2: Isp 350 s, wet 120,000 kg, dry 20,000 kg. ln(6) = 1.792, so Δv2 = 350 × 9.80665 × 1.792 = 6,149.9 m/s. Total: 3,305.9 + 6,149.9 = 9,455.8 m/s.

Try this example →

Common mistakes

  • Entering stage 1's wet mass as the booster alone. It must be the whole vehicle at liftoff, and the stage 1 dry mass must still contain the second stage and payload. Otherwise Δv1 is overstated.
  • Entering Isp in m/s (effective exhaust velocity) rather than seconds. The tool multiplies by g0 itself, so a figure like 2,700 gives a result about ten times too large.
  • Leaving the payload out of stage 2's dry mass. The payload is still on board when the upper stage burns out, so omitting it overstates Δv2.
  • Mixing mass units between wet and dry, such as kilograms for one and tonnes for the other. Only the ratio matters, so the units must be the same on both.
  • Comparing the total with an orbit's required Δv without losses. Gravity and drag losses are not modelled, so this is an ideal figure and the real vehicle needs a margin above it.

About this calculator

Delta-v is the total change in velocity a rocket can produce by burning its propellant, and it's the single number that determines what a rocket can actually do — reach orbit, transfer to another planet, land, and so on. For a single stage, it's given by the Tsiolkovsky rocket equation: Δv = Isp × g0 × ln(m_wet / m_dry).

Staging — jettisoning empty tanks and engines partway through a burn — exists because dragging dead mass along wastes propellant; a multi-stage rocket's total delta-v is simply the sum of each stage's individual delta-v, computed with that stage's own specific impulse and wet/dry mass ratio. Aerospace engineers designing launch vehicles, along with hobbyists using tools like Kerbal Space Program, use this calculation to check whether a given rocket design has enough performance margin to reach its mission's required delta-v budget.

Was this helpful?

You can pick up to 3 reactions.

Comments

  • Be the first to comment.

Popular calculators

Loan Calculator

Monthly payment, total interest and full amortization schedule.

Percentage Calculator

Percent change, percent of, and ratio calculations.

Discount Calculator

Calculate final price, savings, and discount amount.

BMI Calculator

Body mass index from height and weight (metric or imperial).

Age Calculator

Compute your exact age in years, months and days from a birth date.

Compound Interest Calculator

Calculate the final amount and interest earned with compounding.

All Calculators