🔥 Rocket Nozzle & Thrust Calculator
🔥 Rocket Nozzle & Thrust Calculator
From chamber pressure, temperature, gamma, molar mass and throat size, solve the isentropic nozzle: mass flow, exit Mach, thrust, Isp, c* and the optimum expansion ratio for sea level or vacuum.
Vacuum specific impulse against expansion ratio for this chamber condition and gas. The dashed crosshair marks the expansion ratio entered.
Nozzle and performance detail
The isentropic equations, the frozen-flow assumption, and why real Isp is lower
Characteristic velocity. For an ideal gas with stagnation pressure pc and temperature Tc, the mass flow through a choked throat is set by c* = √(R Tc/γ) · ((γ+1)/2)(γ+1)/(2(γ−1)), and ṁ = pcAt/c*. c* is a property of the propellant and chamber condition, not of the nozzle shape downstream of the throat. The tool uses R = 8,314.46/M with M in kg/kmol.
Expansion. The area–Mach relation A/A* = (1/M)[(2/(γ+1))(1 + (γ−1)M²/2)](γ+1)/(2(γ−1)) is solved on the supersonic branch for the exit Mach number. Exit pressure and temperature follow from the isentropic relations, exit velocity from ve = √(2cp(Tc−Te)), and thrust from F = ṁve + (pe−pa)Ae. The pressure term is why the same nozzle makes more thrust in vacuum than at sea level, and why a sea-level-optimised nozzle is under-expanded above the atmosphere.
Optimum expansion. Thrust from a fixed chamber condition is maximised when the exit pressure equals ambient pressure. In vacuum the ideal expansion ratio is infinite, but real nozzles are finite because of size, weight and separation limits. The optimum shown here uses the pressure ratio pc/pa and the same area–Mach relation.
Assumptions and losses. The model assumes a calorically perfect gas, frozen composition, one-dimensional isentropic flow, no boundary-layer blockage, no divergence loss, no combustion inefficiency and uniform chamber conditions. Real engines typically deliver 2–8% less Isp: a 15° half-angle bell loses about 1.7% to divergence, wall friction and heat transfer take more, and shifting combustion equilibrium can move c* by a few percent. Use NASA CEA, RPA or a validated engine model for hardware design, and never size a pressure vessel from a browser calculation.
Flow separation. A strongly over-expanded nozzle can separate: the boundary layer detaches from the wall and the flow becomes asymmetric and unsteady, with side loads that can damage a real nozzle. A common screening criterion is pe < 0.4 pa (Summerfield). This tool flags it but does not model the separated flow.
Last reviewed: 2026-10-19. An ideal-cycle teaching and preliminary-sizing tool, not a substitute for hot-fire data or a qualified propulsion analysis.