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<!doctype html>
<html lang="en">
<head>
<meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1">
<title>Time Dilation Calculator</title>
<link rel="icon" href="favicon.ico" type="image/x-icon">
<link rel="stylesheet" href="assets/css/bootstrap.css">
<link rel="stylesheet" href="assets/css/style.css" type="text/css">
<link rel="stylesheet" href="assets/css/style_gamma.css" type="text/css">
<link rel="stylesheet" href="assets/css/fontawesome.css">
<link rel="stylesheet" href="assets/fontawesome/css/brands.css">
<link rel="stylesheet" href="assets/fontawesome/css/solid.css">
</head>
<body class="bg-pcode">
<header>
<div class="header"></div>
</header>
<section class="container">
<div class="jumbotron jumbotron-fluid mt-1 mb-1 shadow p-3 jumbo-bg">
<div class="container">
<h1 class="display-4 text-center text-wrap">Time Dilation Calculator</h1>
<p class="lead">Calculate the time dilation effect, where time appears to pass slower for objects moving at high velocities compared to those at rest, according to the theory of special relativity. The calculator allows you to determine the amount of
time dilation experienced by an object moving at a certain velocity relative to an observer, or the velocity required to achieve a certain amount of time dilation.</p>
<p>Begin by selecting the known variables to calculate the unknown quantity.</p>
</div>
</div>
</section>
<section class="container border border-info bg_cont mb-1">
<div class="row">
<h3 class="d-flex justify-content-center">Equation</h3>
</div>
\begin{equation*} \Large \Delta t = \frac{\Delta t_0}{\sqrt{1 - \frac{v^2}{c^2}}} \end{equation*}
</section>
<form id="SubmissionForm" novalidate>
<!-- Equation Selection -->
<section class="container border border-primary bg_cont mb-1">
<h4>Select the things you know:
<a tabindex="0" class="btn btn-link" role="button" data-bs-toggle="popover" data-bs-trigger="focus" data-bs-title="Select known variables" data-bs-content="By getting you to select the known variables you can start to become more familiar with the equations. You can select any two variables to calculate the third.">
<small><i class="far fa-question-circle fa"></i></small>
</a>
</h4>
<p>Please note that this calculator converts all inputs into SI or metric units. Select the variables that you know and calculate for the remaining variable. You can change your selection later if you want. This will help you become familiar
with the processes of calculating pressure equations.</p>
<p>For more information about the time dilation calculator, please visit our <a href="https://#" target="_blank" rel="noopener">time dilation</a> page.
</p>
<!-- Check Boxes -->
<div class="row align-items-center">
<div class="col-3 text-center">
<p class="fs-5 mb-0"><i class="fas text-warning fa-check-square me-2"></i>Select the variables you know:
</p>
</div>
<div class="col-9">
<div class="ideal-check border p-3">
<div class="form-check form-switch border-bottom">
<input class="form-check-input" type="checkbox" value="time" id="time" name="time">
<label class="form-check-label" for="time">
Dilated Time (∆t)
</label>
</div>
<div class="form-check form-switch border-bottom">
<input class="form-check-input" type="checkbox" value="properTime" id="properTime" name="properTime">
<label class="form-check-label" for="properTime">
Proper Time (∆t₀)
</label>
</div>
<div class="form-check form-switch border-bottom">
<input class="form-check-input" type="checkbox" value="velocity" id="velocity" name="velocity">
<label class="form-check-label" for="velocity">
Velocity (v)
</label>
</div>
</div>
</div>
</div>
</section>
<section class="container border border-primary bg_cont">
<div class="row d-flex justify-content-center">
<div class="card shadow-sm p-3 mt-1 mb-1" style="width: 32rem;">
<i class="fa-solid fa-clock-rotate-left fa-10x rounded mx-auto d-block mt-1 shadow-sm p-3"></i>
<div class="card-body">
<h4 class="text-center">Time Dilation<br>
</h4>
<!-- Input 1 Dilated Time -->
<div class="form-group">
<div class="row">
<div class="col-7">
<label for="inputTime" class="form-label d-none d-sm-inline">Dilated Time
(∆t)</label>
<a tabindex="0" class="btn btn-link" data-bs-toggle="popover" data-bs-trigger="focus" data-bs-title="Dilated Time (∆t):" data-bs-content="Enter the time in units of seconds (s), minutes (min), hours
(h), days (d), weeks (wk), months (mo), or years (yr). Example: 3600 s or 1 h
for a time
of 1 hour.<br>
Dilated time is the difference in the passage of time between two observers in
relative motion. When an object moves at high speeds, time for that object
appears to slow down relative to a stationary observer. This phenomenon is
called time dilation.<br>
Proper time, on the other hand, is the time that is measured by an observer who
is at rest relative to the object being measured. It is sometimes called the
'true' or 'physical' time experienced by the object. Proper time is always less
than or equal to the dilated time measured by observers in relative motion.<br>
In other words, dilated time is the time measured by observers who are moving
relative to the object, while proper time is the time measured by an observer
who is at rest relative to the object.">
<i class="far fa-question-circle fa"></i>
</a>
<input type="number" name="inputTime" id="inputTime" class="reset_form formCheck maxAllow form-control input-rounded-start" aria-label="Enter the time in units of seconds (s), minutes (min), hours (h),
days
(d), weeks (wk), months (mo), or years (yr)." data-input="time" value="" max="1e15" min="1e-24" step="any" autocomplete="off" disabled placeholder="Dilated Time (∆t)">
</div>
<div class="col-5">
<label for="unitsTime" class="form-label">Units</label>
<select class="form-select form-control" name="unitsTime" id="unitsTime" data-input="time" disabled>
<option value="yr" selected>yr</option>
<option value="s">s</option>
<option value="min">min</option>
<option value="h">h</option>
<option value="d">d</option>
<option value="wk">wk</option>
<option value="mo">mo</option>
<option value="ms">ms</option>
<option value="μs">μs</option>
<option value="ns">ns</option>
</select>
</div>
</div>
</div>
<!-- Input 2 Proper Time -->
<div class="form-group">
<div class="row">
<div class="col-7">
<label for="inputProperTime" class="form-label d-none d-sm-inline">Proper Time
(∆t₀)</label>
<a tabindex="0" class="btn btn-link" data-bs-toggle="popover" data-bs-trigger="focus" data-bs-title="Proper Time (∆t₀):" data-bs-content="Enter the time in units of seconds (s), minutes (min), hours
(h), days (d), weeks (wk), months (mo), or years (yr). Example: 3600 s or 1 h for a time
of 1 hour.<br>
Dilated time is the difference in the passage of time between two observers in
relative motion. When an object moves at high speeds, time for that object
appears to slow down relative to a stationary observer. This phenomenon is
called time dilation.<br>
Proper time, on the other hand, is the time that is measured by an observer who
is at rest relative to the object being measured. It is sometimes called the
'true' or 'physical' time experienced by the object. Proper time is always less
than or equal to the dilated time measured by observers in relative motion.<br>
In other words, dilated time is the time measured by observers who are moving
relative to the object, while proper time is the time measured by an observer
who is at rest relative to the object.">
<i class="far fa-question-circle fa"></i>
</a>
<input type="number" name="inputProperTime" id="inputProperTime" class="reset_form formCheck maxAllow form-control input-rounded-start" aria-label="Enter the time in units of seconds (s), minutes (min), hours (h),
days
(d), weeks (wk), months (mo), or years (yr)." data-input="properTime" value="" max="1e15" min="1e-24" step="any" autocomplete="off" disabled placeholder="Proper Time (∆t₀)">
</div>
<div class="col-5">
<label for="unitsProperTime" class="form-label">Units</label>
<select class="form-select form-control" name="unitsProperTime" id="unitsProperTime" data-input="properTime" disabled>
<option value="yrp" selected>yr</option>
<option value="sp">s</option>
<option value="minp">min</option>
<option value="hp">h</option>
<option value="dp">d</option>
<option value="wkp">wk</option>
<option value="mop">mo</option>
<option value="msp">ms</option>
<option value="μsp">μs</option>
<option value="nsp">ns</option>
</select>
</div>
</div>
</div>
<!-- Input 3 - Velocity -->
<div class="form-group">
<div class="row">
<div class="col-7">
<label for="inputVelocity" class="form-label d-none d-sm-inline">Velocity
(v)</label>
<a tabindex="0" class="btn btn-link" data-bs-toggle="popover" data-bs-trigger="focus" data-bs-title="Velocity (c):" data-bs-content="Enter
the velocity of the object in a
decimal of the speed of light (c), and the calculator will automatically compute
the corresponding gamma factor. The gamma factor is a key component of the
Lorentz equations that describe the effects of relativity on time, space, and
energy. Example: 0.5 for half the speed of light, or 0.866 for 86.6% the speed of
light.">
<i class="far fa-question-circle fa"></i>
</a>
<input type="number" name="inputVelocity" id="inputVelocity" class="reset_form formCheck maxAllow form-control input-rounded-start" aria-label="Enter the velocity of the object in a decimal of the speed of light
(c), and the calculator will automatically compute the corresponding gamma
factor. The gamma factor is a key component of the Lorentz equations that
describe the effects of relativity on time, space, and energy. Example: 0.5 for
half the speed of light, or 0.866 for 80% the speed of light." data-input="velocity" value="" min="0" max="0.999999999999999" step="1e-16" autocomplete="off" disabled placeholder="Velocity (v)">
</div>
<div class="col-5">
<label for="unitsVelocity" class="form-label">Units</label>
<select class="form-select form-control" name="unitsVelocity" id="unitsVelocity" data-input="velocity" disabled>
<option value="c" selected>c</option>
<option value="ms">ms⁻¹</option>
<option value="kmh">kmh⁻¹</option>
<option value="mph">mph</option>
<option value="kms">kms⁻¹</option>
</select>
</div>
</div>
</div>
</div>
</div>
</div>
<div class="col text-center">
<button type="reset" class="btn-sm btn-outline-danger btn mb-2" id="resetButton1">Reset</button>
<a tabindex="0" class="btn btn-link" role="button" data-bs-toggle="popover" data-bs-trigger="focus" data-bs-title="Reset Form" data-bs-content="Reset the form to add new variables to calculate.">
<i class="far fa-question-circle fa mb-2"></i>
</a>
<button type="button" class="btn-sm btn btn-outline-success mb-2" id="submitButton" disabled>Calculate</button>
<a tabindex="0" class="btn btn-link" role="button" data-bs-toggle="popover" data-bs-trigger="focus" data-bs-title="Calculate" data-bs-content="Once you have added three variables submit the calculation for evaluation.">
<i class="far fa-question-circle fa mb-2"></i>
</a>
<div id="error"></div>
</div>
<br>
</section>
<!-- TABLE ONE - RESULTS -->
<section id="results_table_1" class="container border border-success mt-1 mb-1 bg_cont">
<h5>Table 1: Results in SI units</h5>
<table class="table table-sm">
<thead>
<tr>
<th scope="col" class="w50">Variable</th>
<th scope="col" class="w50">Amount</th>
</tr>
</thead>
<tbody>
<tr>
<td>Gamma (γ)</td>
<td id="gammaOutput">(dimensionless)</td>
</tr>
<tr>
<td>Velocity (v)</td>
<td id="velocityOutput">c</td>
</tr>
<tr>
<td>Dilated Time (∆t)</td>
<td id="timeOutput">years</td>
</tr>
<tr>
<td>Proper Time (∆t₀)</td>
<td id="properTimeOutput">years</td>
</tr>
</tbody>
</table>
<h6 class="equation_color">Equation Used:</h6>
<p id="equation"></p>
<p id="substitutedNumbers"></p>
<button type="reset" class="btn-sm btn-outline-danger btn mb-2" id="resetButton2">Reset</button>
<a tabindex="0" class="btn btn-link" role="button" data-bs-toggle="popover" data-bs-trigger="focus" data-bs-title="Reset Form" data-bs-content="Reset the form to add new variables to calculate. The answer will remain here until you calculate a new set of variables.">
<i class="far fa-question-circle fa mb-2"></i>
</a>
<br>
<p><em>Table 1 provides the SI unit for each variable. Note that the gamma factor (γ) is a dimensionless
unit. You can change the
output accordingly and see the
common unit conversions in Table 2.</em></p>
</section>
</form>
<!-- Table 2 Results Table -->
<section class="container border border-success mt-1 mb-2 bg_cont">
<h5>Table 2: Results with common units displayed</h5>
<table class="table table-sm">
<thead>
<tr class="t_line">
<th scope="col" class="w50">Variable</th>
<th scope="col" class="w50">Amount</th>
</tr>
</thead>
<tbody>
<tr class="t_line">
<td>Gamma (γ)</td>
<td id="g1x">c</td>
</tr>
<tr>
<td>Velocity (v)</td>
<td id="v1x">ms<sup>-1</sup></td>
</tr>
<tr>
<td></td>
<td id="v0x">c</td>
</tr>
<tr>
<td></td>
<td id="v2x">kmh<sup>-1</sup></td>
</tr>
<tr>
<td></td>
<td id="v3x">fts<sup>-1</sup></td>
</tr>
<tr>
<td></td>
<td id="v4x">knots</td>
</tr>
<tr>
<td></td>
<td id="v5x">kms<sup>-1</sup></td>
</tr>
<tr class="t_line">
<td></td>
<td id="v6x">cms<sup>-1</sup></td>
</tr>
<tr>
<td>Dilated Time (∆t)</td>
<td id="t1x">s</td>
</tr>
<tr>
<td></td>
<td id="t3x">min</td>
</tr>
<tr>
<td></td>
<td id="t4x">hr</td>
</tr>
<tr>
<tr>
<td></td>
<td id="t5x">days</td>
</tr>
<tr>
<td></td>
<td id="t6x">weeks</td>
</tr>
<tr>
<td></td>
<td id="t7x">months</td>
</tr>
<tr>
<td></td>
<td id="t8x">years</td>
</tr>
<tr>
<td></td>
<td id="t9x">ms</td>
</tr>
<tr>
<td></td>
<td id="t10x">μs</td>
</tr>
<tr>
<td></td>
<td id="t11x">ns</td>
</tr>
<tr class="t_line">
<tr>
<td>Proper Time (∆t₀)</td>
<td id="pt1x">s</td>
</tr>
<tr>
<td></td>
<td id="pt3x">min</td>
</tr>
<tr>
<td></td>
<td id="pt4x">hr</td>
</tr>
<tr>
<tr>
<td></td>
<td id="pt5x">days</td>
</tr>
<tr>
<td></td>
<td id="pt6x">weeks</td>
</tr>
<tr>
<td></td>
<td id="pt7x">months</td>
</tr>
<tr>
<td></td>
<td id="pt8x">years</td>
</tr>
<tr>
<td></td>
<td id="pt9x">ms</td>
</tr>
<tr>
<td></td>
<td id="pt10x">μs</td>
</tr>
<tr>
<td></td>
<td id="pt11x">ns</td>
</tr>
<tr class="t_line">
</tbody>
</table>
<p><em>Table 2 shows the results of all the calculations and various units available with all conversions
completed.</em>
</p>
</section>
</div>
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<div id="alert-box" role="alert" aria-label="Alert: Invalid input.">
<span id="alert-message">Invalid input.</span>
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