Percentage of Light Speed (% of c)
Meters per second (m/s)
Kilometers per second (km/s)
Kilometers per hour (km/h)
Miles per hour (mph)
Results:
Lorentz Factor (γ):
–
Time Dilation Factor:
–
Length Contraction:
–
Velocity as fraction of c:
–
What is the Lorentz Factor?
The Lorentz factor (denoted by the Greek letter γ, gamma) is a quantity used in special relativity to describe how much time, length, and relativistic mass change for an object while that object is moving. It is a fundamental component of Einstein's equations and becomes significant only as speeds approach the speed of light.
The Formula
γ = 1 / √(1 – v²/c²)
Where:
v is the relative velocity between inertial reference frames.
c is the speed of light in a vacuum (approx. 299,792,458 m/s).
γ is the resulting Lorentz factor.
Practical Examples of γ
In our everyday lives, the Lorentz factor is nearly exactly 1. However, in particle accelerators or deep-space theoretical physics, it increases dramatically:
Speed (v)
Lorentz Factor (γ)
Effect
10% Light Speed (0.1c)
1.005
0.5% Change
86.6% Light Speed (0.866c)
2.000
Time moves half as fast
99% Light Speed (0.99c)
7.089
Significant dilation
99.9% Light Speed (0.999c)
22.366
Extreme relativistic mass
Relativistic Implications
Time Dilation: An observer will see a clock moving relative to them as ticking slower by a factor of γ. This has been proven with highly accurate atomic clocks flown on jets and satellites (GPS systems must actually account for this!).
Length Contraction: Objects moving at high speeds appear shorter in the direction of motion to a stationary observer. A 100-meter spaceship moving at 0.866c would appear only 50 meters long.
Mass-Energy: As γ increases, the kinetic energy of an object increases. To accelerate an object with mass to exactly the speed of light would require infinite energy, as the Lorentz factor becomes infinite.
function calculateLorentzFactor() {
var vInput = document.getElementById("velocityValue").value;
var unit = document.getElementById("velocityUnit").value;
var resultDiv = document.getElementById("lorentzResult");
var gammaOutput = document.getElementById("gammaOutput");
var timeDilation = document.getElementById("timeDilation");
var lengthContraction = document.getElementById("lengthContraction");
var betaValue = document.getElementById("betaValue");
var warning = document.getElementById("physicsWarning");
if (!vInput || vInput === "") {
alert("Please enter a valid velocity.");
return;
}
var v = parseFloat(vInput);
var c = 299792458; // Speed of light in m/s
var beta = 0; // v/c ratio
// Convert input to beta (v/c)
if (unit === "percentage") {
beta = v / 100;
} else if (unit === "ms") {
beta = v / c;
} else if (unit === "kms") {
beta = (v * 1000) / c;
} else if (unit === "kmh") {
beta = (v / 3.6) / c;
} else if (unit === "mph") {
beta = (v * 0.44704) / c;
}
// Calculations
if (beta >= 1) {
resultDiv.style.display = "block";
gammaOutput.innerHTML = "Undefined";
timeDilation.innerHTML = "Infinite";
lengthContraction.innerHTML = "0%";
betaValue.innerHTML = (beta).toFixed(6) + " c";
warning.style.display = "block";
warning.innerHTML = "Error: Velocity cannot reach or exceed the speed of light (c) for objects with mass.";
} else if (beta < 0) {
alert("Velocity cannot be negative in this context. Using absolute value.");
document.getElementById("velocityValue").value = Math.abs(v);
calculateLorentzFactor();
} else {
var gamma = 1 / Math.sqrt(1 – Math.pow(beta, 2));
var contraction = (1 / gamma) * 100;
resultDiv.style.display = "block";
warning.style.display = "none";
// Format results
gammaOutput.innerHTML = gamma.toLocaleString(undefined, {maximumFractionDigits: 6});
timeDilation.innerHTML = gamma.toLocaleString(undefined, {maximumFractionDigits: 4}) + "x";
lengthContraction.innerHTML = contraction.toFixed(2) + "% of original";
betaValue.innerHTML = (beta).toFixed(6) + " c";
}
}