The FTL Rate Calculator is designed for science fiction enthusiasts, writers, and theoretical physics hobbyists to determine the travel time required to traverse vast interstellar distances using hypothetical propulsion systems. Unlike standard kinematic calculators, this tool operates on scales defined by the speed of light ($c$).
How FTL Speed is Measured
In most contexts, Faster-Than-Light speed is measured in multiples of $c$ (where $c \approx 299,792,458$ meters per second). However, science fiction often uses a "Warp Factor" scale. This calculator primarily uses the scale popularized by Star Trek: The Next Generation (TNG), which is non-linear.
Warp 1: Exactly the speed of light ($1c$).
Warp 5: Approximately $213c$.
Warp 9: Approximately $1,516c$.
Warp 9.9: Approximately $3,053c$.
Calculation Formulas
To calculate the travel time, we first normalize all inputs to standard astronomical units.
1. Distance Normalization:
All distances are converted to Light Years (ly).
1 Parsec $\approx$ 3.26 ly.
1 AU (Astronomical Unit) $\approx$ 0.0000158 ly.
2. Velocity Calculation:
If using Warp Factors (W), the velocity ($v$) in multiples of $c$ is calculated using the TNG approximation formula:
$$ v = W^{(10/3)} $$
For inputs utilizing direct multiples of light speed, the value is used as-is.
3. Time Calculation:
$$ \text{Time (Years)} = \frac{\text{Distance (ly)}}{\text{Velocity (c)}} $$
The result is then converted into Days, Hours, and Minutes for easier readability.
Example Scenarios
Trip to Alpha Centauri: The nearest star system is roughly 4.37 light years away. Traveling at Warp 5 ($213c$), the trip would take approximately 7.5 days.
Crossing the Milky Way: Our galaxy is approximately 100,000 light years in diameter. Even at a staggering speed of Warp 9.9 ($3,053c$), traversing the entire galaxy would still take nearly 33 years.
// Inline JavaScript for FTL Calculation
// Helper functions to set preset values
function setDist(val, unit) {
document.getElementById('ftl_distance').value = val;
document.getElementById('ftl_dist_unit').value = unit;
}
function setSpeed(val) {
document.getElementById('ftl_speed').value = val;
// Default to Warp for presets, unless changed
document.getElementById('ftl_speed_type').value = 'warp_tng';
}
function toggleSpeedLabel() {
var type = document.getElementById('ftl_speed_type').value;
var presetContainer = document.getElementById('speed_presets');
// Just clearing presets visual if switching to C multiples as warp presets make less sense contextually
if(type === 'c_multiple') {
presetContainer.style.opacity = '0.5';
presetContainer.style.pointerEvents = 'none';
} else {
presetContainer.style.opacity = '1';
presetContainer.style.pointerEvents = 'auto';
}
}
function calculateFTL() {
// 1. Get Inputs
var distInput = parseFloat(document.getElementById('ftl_distance').value);
var distUnit = document.getElementById('ftl_dist_unit').value;
var speedInput = parseFloat(document.getElementById('ftl_speed').value);
var speedType = document.getElementById('ftl_speed_type').value;
// 2. Validate Inputs
if (isNaN(distInput) || isNaN(speedInput) || distInput <= 0 || speedInput <= 0) {
alert("Please enter valid positive numbers for distance and speed.");
return;
}
// 3. Normalize Distance to Light Years (ly)
var distanceLY = 0;
if (distUnit === 'ly') {
distanceLY = distInput;
} else if (distUnit === 'pc') {
distanceLY = distInput * 3.26156;
} else if (distUnit === 'au') {
distanceLY = distInput * 0.0000158125;
}
// 4. Calculate Velocity in Multiples of C
var velocityC = 0;
if (speedType === 'c_multiple') {
velocityC = speedInput;
} else if (speedType === 'warp_tng') {
// Formula: v = w^(10/3)
// Limit warp to = 10) {
velocityC = Infinity;
} else {
velocityC = Math.pow(speedInput, (10/3));
}
}
// 5. Calculate Time
// Time (Years) = Distance (LY) / Velocity (c)
var timeYears = 0;
if (velocityC === Infinity) {
timeYears = 0;
} else {
timeYears = distanceLY / velocityC;
}
// 6. Convert Time to readable units
var timeDays = timeYears * 365.25;
var timeHours = timeDays * 24;
var timeMinutes = timeHours * 60;
var timeSeconds = timeMinutes * 60;
// Determine best display unit
var displayString = "";
if (velocityC === Infinity) {
displayString = "Instantaneous";
} else if (timeYears >= 1000) {
displayString = timeYears.toLocaleString(undefined, {maximumFractionDigits: 0}) + " Years";
} else if (timeYears >= 1) {
var y = Math.floor(timeYears);
var d = Math.floor((timeYears – y) * 365.25);
displayString = y + " Years, " + d + " Days";
} else if (timeDays >= 1) {
var d = Math.floor(timeDays);
var h = Math.floor((timeDays – d) * 24);
displayString = d + " Days, " + h + " Hours";
} else if (timeHours >= 1) {
var h = Math.floor(timeHours);
var m = Math.floor((timeHours – h) * 60);
displayString = h + " Hours, " + m + " Minutes";
} else {
var m = Math.floor(timeMinutes);
var s = Math.floor((timeMinutes – m) * 60);
displayString = m + " Minutes, " + s + " Seconds";
}
// 7. Update UI
document.getElementById('res_velocity').innerText = (velocityC === Infinity ? "Infinite" : velocityC.toLocaleString(undefined, {maximumFractionDigits: 2})) + " c";
document.getElementById('res_distance').innerText = distanceLY.toLocaleString(undefined, {maximumFractionDigits: 4}) + " ly";
document.getElementById('res_time').innerText = displayString;
document.getElementById('res_years').innerText = (velocityC === Infinity ? "0" : timeYears.toLocaleString(undefined, {maximumFractionDigits: 6})) + " Years";
// Show results
document.getElementById('ftl-results').style.display = 'block';
}