Four-Vector Calculator
Calculate Lorentz transformations and invariants for four-vectors
Original Frame (S)
X⁰ (ct or E/c)
2.9980e+8
X¹
1.0000e+8
X²
0.0000e+0
X³
0.0000e+0
Boosted Frame (S') - β = 0.333556, γ = 1.060749
X'⁰
2.8263e+8
X'¹
0.0000e+0
X'²
0.0000e+0
X'³
0.0000e+0
Lorentz Invariants
Invariant (X·X) in S
7.9880e+16
Invariant (X'·X') in S'
7.9880e+16
Classification
Timelike
✓ Invariant preserved
About Four-Vectors
Four-vectors combine time and space (or energy and momentum) into objects that transform properly under Lorentz transformations. The position four-vector is Xμ = (ct, x, y, z) and the momentum four-vector is Pμ = (E/c, px, py, pz). The invariant X·X = (X⁰)² - (X¹)² - (X²)² - (X³)² is the same in all inertial frames.