Delta V Calculator

What Is Delta V (Δv)?

Delta v (Δv) is the change in velocity of a rocket or spacecraft. It measures how much speed is gained or lost during a burn and is central to orbital mechanics and mission planning.

Rocket Equation

$$\Delta v = I_{sp} \cdot g_0 \cdot \ln\left(\frac{m_0}{m_f}\right)$$

$I_{sp}$ is specific impulse in seconds, $g_0 = 9.80665$ m/s² is standard gravity, $m_0$ is initial mass, and $m_f$ is final mass after propellant is burned.

Impulse Method

$$\Delta v = \frac{J}{m}$$

When impulse $J$ (N·s) and mass $m$ (kg) are known, velocity change equals impulse divided by mass.

Applications

Δv budgets determine whether a rocket can reach orbit, transfer between planets, or perform rendezvous. Mission designers stack Δv requirements for each burn to verify total propellant needs.

Frequently Asked Questions

What is specific impulse (Isp)?

Specific impulse measures rocket engine efficiency in seconds. Higher Isp means more thrust per unit of propellant consumed.

Why must final mass be less than initial mass?

The rocket equation requires propellant to be expelled. If $m_f \geq m_0$, no propellant was burned and ln(m₀/m_f) is zero or negative.

When should I use the impulse formula?

Use Δv = J/m for short impulses on a fixed mass, such as a collision, kick stage, or known momentum transfer where Isp and mass ratio are not relevant.

What units does this calculator use?

Mass in kilograms, Isp in seconds, impulse in N·s, and Δv in m/s. Standard gravity g₀ is 9.80665 m/s².

Does Δv depend on direction?

Δv is a scalar magnitude of velocity change. Vector direction matters for orbital maneuvers, but the rocket equation gives the speed change from a burn.

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What Is Delta V (Δv)?

Rocket Equation

Impulse Method

Applications

Frequently Asked Questions

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