Adding up a budget
Unlike a single Hohmann transfer or a single Tsiolkovsky burn, a mission Δv budget is a list. Typical lines are gravity loss and drag loss during ascent, steering or residuals, orbital insertion or circularization, a plane change, mid-course corrections, a landing or braking burn, and a reserve. This page totals whatever you name. A low-Earth-orbit plus 30° plane-change example is in the loaded template: the plane-change term alone at 7.67 km/s is about 3.97 km/s — often larger than the Hohmann legs — which is why combined burns are used in practice.
The total is a scalar sum of non-negative items. It is not a vector, and it does not know whether two burns could have been combined. For a two-impulse coplanar transfer, use the Hohmann transfer calculator and paste those Δv values in as lines.
Mass ratio and plane change
If you enter a specific impulse, the ideal (massless-losses) rocket equation converts the budget to a mass ratio, with the same g0 = 9.80665 m/s² used on the rocket-equation and specific-impulse pages:
m0/mf = exp( Δv / (Isp × g0) )
A 9.5 km/s budget at 300 s Isp is a mass ratio of about 25.3, or a propellant fraction of about 0.96 — before any structural mass. That is a planning bound, not a vehicle design.
A pure impulsive plane change at speed V through an angle θ costs
Δv = 2 V sin(θ/2)
Doing the plane change at a slower apogee, or combining it with a Hohmann burn, reduces that cost; those combined maneuvers are not modelled here.
Sources
Vallado, Fundamentals of Astrodynamics and Applications (impulsive Δv, plane-change formula); Curtis, Orbital Mechanics for Engineering Students; Sutton and Biblarz, Rocket Propulsion Elements (Tsiolkovsky mass ratio). For individual burns, see this site's Hohmann transfer and rocket equation calculators.
Frequently asked questions
What is a 30° plane change at 7.67 km/s?
About 3.970 km/s. The impulsive formula is Δv = 2 V sin(θ/2) = 2 × 7.67 × sin(15°) km/s. That is a pure plane change at that speed, not a combined Hohmann-plus-plane-change burn.
What mass ratio does 9.5 km/s at 300 s Isp require?
About 25.3, in the ideal rocket equation with ve = Isp × 9.80665 m/s². The matching propellant fraction is 1 − 1/25.3 ≈ 0.96, before structure or residuals.
Can I paste a Hohmann Δv into this budget?
Yes. Compute the two impulses on the Hohmann transfer page, then enter them as named items here, along with losses, a plane change, and a reserve, to get a mission total and an ideal mass ratio.