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Physics

Rocket Δv (Tsiolkovsky)

Δv = Isp × g₀ × ln(m₀/mf). Free online Rocket Δv (Tsiolkovsky). Calculate rocket δv (tsiolkovsky) online — fast, accurate, mobile-friendly, no signup needed.

Δv (m/s)
3,542.08197

Derivation

  1. ├── 01Givenisp = 300, m0 = 1000, mf = 300
  2. ├── 02Formula9.80665 × t × ln(a / n)
  3. └── 03Compute Δv (m/s)3,542.08197
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§01What is

Understanding the Rocket Δv (Tsiolkovsky)

The Rocket Δv (Tsiolkovsky) computes Δv (m/s) from 3 inputs: isp (s), initial mass (kg), final mass (kg). Δv = Isp × g₀ × ln(m₀/mf).

Physics is the toolkit for turning a real-world observation into a prediction. Whether it’s a falling object, a moving car, or a stressed beam, the equations here are the same ones every engineer relies on. The Rocket Δv (Tsiolkovsky) sits in that toolkit — it Δv = Isp × g₀ × ln(m₀/mf). Enter your numbers above and the result updates instantly; every step of the math is shown in the Derivation panel so you can see exactly how the answer was reached.

§02The Formula

How it’s calculated

9.80665 × t × ln(a / n)

Where

isp
Isp (s)
m0
Initial mass (kg)
mf
Final mass (kg)
§03Practical Example

Step-by-step walkthrough

Scenario

Apply the formula to a realistic set of inputs: Isp (s) = 300, Initial mass (kg) = 1000, Final mass (kg) = 300.

  1. 01Start by noting the input — Isp (s): 300.
  2. 02Start by noting the input — Initial mass (kg): 1000.
  3. 03Start by noting the input — Final mass (kg): 300.
  4. 04Substitute these values into the formula: 9.80665 × t × ln(a / n)
  5. 05Compute Δv (m/s): the calculator returns 3542.08.
  6. 06Cross-check the answer by opening the Derivation panel above — every line of math is shown so you can follow the computation end-to-end.
§04Variants

Common Rocket Δv (Tsiolkovsky) Problems

The formula gets rearranged depending on which variable you need. Here are the patterns you’ll run into in the real world — find the one that matches your problem and follow the worked steps.

01 · PATTERN

Isp (s) halved

isp = 150 (from 300)

Keep every other input at its default and halve the isp (s). See how δv (m/s) responds.

  1. 01New Isp (s): 150
  2. 02Baseline Δv (m/s): 3542.08
  3. 03New Δv (m/s): 1771.04
  4. 04Δv (m/s) decreases by 50% → use this sensitivity to plan for real-world variation.
02 · PATTERN

Isp (s) doubled

isp = 600 (from 300)

Keep every other input at its default and double the isp (s). See how δv (m/s) responds.

  1. 01New Isp (s): 600
  2. 02Baseline Δv (m/s): 3542.08
  3. 03New Δv (m/s): 7084.16
  4. 04Δv (m/s) increases by 100% → use this sensitivity to plan for real-world variation.
03 · PATTERN

Initial mass (kg) halved

m0 = 500 (from 1000)

Keep every other input at its default and halve the initial mass (kg). See how δv (m/s) responds.

  1. 01New Initial mass (kg): 500
  2. 02Baseline Δv (m/s): 3542.08
  3. 03New Δv (m/s): 1502.85
  4. 04Δv (m/s) decreases by 57.6% → use this sensitivity to plan for real-world variation.
04 · PATTERN

Initial mass (kg) doubled

m0 = 2000 (from 1000)

Keep every other input at its default and double the initial mass (kg). See how δv (m/s) responds.

  1. 01New Initial mass (kg): 2000
  2. 02Baseline Δv (m/s): 3542.08
  3. 03New Δv (m/s): 5581.32
  4. 04Δv (m/s) increases by 57.6% → use this sensitivity to plan for real-world variation.
§05FAQ

Frequently asked questions

Yes. The calculator implements the standard formula as documented and returns exact floating-point results. No approximations are used unless noted in the formula.
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