Scientific Calculator
Aerospace Constants
Common physical constants for aerospace calculations
Earth RadiusR_E
6.371 × 10⁶ m
Gravitational Parameterμ_E
3.986 × 10¹⁴ m³/s²
Speed of Lightc
2.998 × 10⁸ m/s
Boltzmann Constantk_B
1.381 × 10⁻²³ J/K
Avogadro's NumberN_A
6.022 × 10²³ mol⁻¹
Universal Gas ConstantR
8.314 J/(mol·K)
Planck Constanth
6.626 × 10⁻³⁴ J·s
Stefan-Boltzmann Constantσ
5.670 × 10⁻⁸ W/(m²·K⁴)
Common Formulas
A categorized list of frequently used engineering and aerospace formulas
Velocity (linear)Kinematics
v = v₀ + a t
Displacement (linear)Kinematics
s = v₀ t + ½ a t²
Velocity-squaredKinematics
v² = v₀² + 2 a s
Uniform motionKinematics
x = x₀ + v t
Angular velocityKinematics
ω = ω₀ + α t
Angular displacementKinematics
θ = ω₀ t + ½ α t²
Angular velocity-squaredKinematics
ω² = ω₀² + 2 α θ
Centripetal accelerationKinematics
a_c = v² / r = ω² r
Newton's 2nd lawDynamics
F = m a
MomentumDynamics
p = m v
ImpulseDynamics
J = ∫ F dt = Δp
Work (line integral)Dynamics
W = ∫ F · ds
PowerDynamics
P = dW/dt = F · v
Kinetic energyDynamics
E_k = ½ m v²
Rotational KEDynamics
E_rot = ½ I ω²
Potential energy (near Earth)Dynamics
E_p = m g h
TorqueDynamics
τ = r × F
Rotational dynamicsDynamics
∑τ = I α
Force equilibriumStatics
∑F = 0
Moment equilibriumStatics
∑M = 0
Friction limitStatics
F_f ≤ μ N
Ideal gas (molar)Thermodynamics
p V = n R T
Ideal gas (specific)Thermodynamics
p v = R T
First law (closed)Thermodynamics
ΔU = Q − W
Internal energyThermodynamics
U = m c_v T
EnthalpyThermodynamics
h = u + p v
Enthalpy (cp)Thermodynamics
H = m c_p T
Specific heatsThermodynamics
c_p − c_v = R
Adiabatic relationThermodynamics
p v^γ = const
Isentropic T ratioThermodynamics
T₂/T₁ = (p₂/p₁)^{(γ−1)/γ}
Isentropic density ratioThermodynamics
ρ₂/ρ₁ = (p₂/p₁)^{1/γ}
Continuity (incompressible)Fluids & Aero
A₁ V₁ = A₂ V₂
BernoulliFluids & Aero
p + ½ ρ v² + ρ g h = const
Dynamic pressureFluids & Aero
q = ½ ρ v²
Reynolds numberFluids & Aero
Re = ρ v L / μ
Speed of soundFluids & Aero
a = √(γ R T)
Mach numberFluids & Aero
M = v / a
Lift forceFluids & Aero
L = ½ ρ v² C_L A
Drag forceFluids & Aero
D = ½ ρ v² C_D A
Skin friction (turbulent plate)Fluids & Aero
C_f ≈ 0.026 Re^{−1/7}
Stagnation pressureFluids & Aero
p₀/p = (1 + (γ−1) M² / 2)^{γ/(γ−1)}
Stagnation temperatureFluids & Aero
T₀/T = 1 + (γ−1) M² / 2
Isentropic densityFluids & Aero
ρ₀/ρ = (1 + (γ−1) M² / 2)^{1/(γ−1)}
Vis-vivaOrbital Mechanics
v² = μ (2/r − 1/a)
Circular orbit speedOrbital Mechanics
v_c = √(μ / r)
Escape speedOrbital Mechanics
v_e = √(2 μ / r)
Orbital periodOrbital Mechanics
T = 2 π √(a³ / μ)
Specific energyOrbital Mechanics
ε = − μ/(2 a)
Specific ang. momentumOrbital Mechanics
h = √(μ a (1 − e²))
Periapsis radiusOrbital Mechanics
r_p = a (1 − e)
Apoapsis radiusOrbital Mechanics
r_a = a (1 + e)
Hohmann Δv₁Orbital Mechanics
Δv₁ = √(μ/r₁) (√(2 r₂/(r₁+r₂)) − 1)
Hohmann Δv₂Orbital Mechanics
Δv₂ = √(μ/r₂) (1 − √(2 r₁/(r₁+r₂)))
Plane changeOrbital Mechanics
Δv = 2 v sin(Δi/2)
Mean motionOrbital Mechanics
n = √(μ / a³)
DensityAtmosphere
ρ = p / (R T)
ISA lapse (troposphere)Atmosphere
T = T₀ − L h
Pressure vs altitudeAtmosphere
p = p₀ (T/T₀)^{g₀/(R L)}
Gravity vs altitudeAtmosphere
g(h) ≈ g₀ (R_E/(R_E+h))²
Scale heightAtmosphere
H = R T / (M g)
Geopotential heightAtmosphere
H_g = (R_E h)/(R_E + h)
Open Source & Transparent
This tool is open source and the underlying logic is fully transparent. You can view the source code, understand the calculations, and even contribute improvements to make it better for everyone.
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