Time Dilation Calculator

• Special Relativity (Speed)

  • Choose a Mode: Select "Special Relativity (Speed)" to calculate time dilation for high-speed space travel.

    • Speed: Use the slider to set the travel speed as a percentage of the speed of light from 0 to 99 percent.

    • Select Distance: Choose a star from the dropdown menu with realistic distances to known celestial bodies or enter a custom distance in light years in the input field.

    • Calculation: Click "Calculate" to compute using Lorentz factor γ = 1/√(1-v²/c²).

    • Result: You will see technical values like the Lorentz factor, travel speed in km per hour and km per second and distance in light years and kilometers. And then you will see the most important time dilation information. It shows the real time that passes for the traveler who is moving at a high fraction of the speed of light and the coordinate time that passes on Earth.

• General Relativity (Gravity):

  • Choose a Mode: Select "General Relativity (Gravity)" for black hole time dilation.

    • Black Hole Mass: Enter solar masses using presets or manual input.

    • Distance from Center: Slider sets multiples of Schwarzschild radius (Rs = 2GM/c²), min 1.01 Rs.

    • Reference Time: Select time period for distant observer.

    • Calculation: Click "Calculate" using τ = t√(1-Rs/r).​

    • Result: You will see technical data like black hole mass, Schwarzschild radius and distance from center. Then the time dilation results showing the proper time near the black hole compared to the reference time for distant observers, along with the dilation factor.

Special Relativity (Speed)

Einstein's special relativity describes how time, length and mass change when objects move at high speeds. The faster an object moves toward the speed of light, the slower time passes for it compared to a stationary observer.

Fundamentals of Time Dilation

Time dilation is an effect of special relativity. The Lorentz factor γ = 1 / √(1 - v²/c²) describes how much time slows down for a moving observer. At 99% light speed, γ ≈ 7.09 - 7 years onboard equal 50 years on Earth.

Light Year as Distance Measure

A light year is the distance that light travels in one year through a vacuum. It is used to express distances in space because stars and galaxies are incredibly far away. One light year equals about 9.46 trillion kilometers. This unit makes it easy to compare and represent distances to distant celestial objects.

Stars in the Tool

The distances to the stars are determined through what are known as parallax measurements. This method tracks the tiny apparent shift of a star in the sky as Earth moves along its orbit around the Sun. With basic geometry, this small shift can be used to calculate the exact distance. Modern space telescopes like Gaia measure these shifts with extremely high precision, which is why the distance values are so accurate. This is how we know that Proxima Centauri is 4.2465 light years away, Sirius is 8.6 light years and Vega is about 25 light years.

Physical Limits

According to Einstein's principle of relativity, no object with mass can reach or exceed the speed of light, so 100% light speed is impossible. The faster an object approaches the speed of light, the more energy is required to continue accelerating it. To reach the speed of light, an object would need infinite energy, which is physically impossible.

Even if it were theoretically possible to give an object infinite energy and reach or exceed the speed of light, the known laws of space and time would break down. Time for the object would run backward and its mass could become negative. Such scenarios lead to paradoxes and are therefore excluded in real-world physics.

General Relativity (Gravity)

Einstein's general relativity explains how gravity curves spacetime. In a strong gravitational field, time passes more slowly. That means a clock near a massive object ticks slower than one far away from it.

Time Dilation Near Massive Objects

The closer you are to a massive object, the slower time passes. For example, a few minutes near a black hole could correspond to years for a distant observer. This effect arises directly from the curvature of spacetime.

Schwarzschild Radius

The Schwarzschild radius, named after the German physicist Karl Schwarzschild who first solved Einstein's equations for a spherical mass, is the critical distance around a mass, such as a black hole, where the escape velocity equals the speed of light. Inside this radius, time would effectively stop from the perspective of a distant observer. The closer you get to this radius, the stronger the time dilation becomes.

Extreme Time Dilation from Movies

Many people know the idea from movies that one hour near a black hole can equal many years far away. This effect can happen in reality, but only under very specific conditions. These conditions go far beyond the simple and easy to understand formulas used in this calculator.

This tool is based on the Schwarzschild solution. It describes time dilation around a non rotating black hole and shows how gravity slows down time as you move closer to a massive object. This approach is widely used in physics because it is clear and reliable.

The extreme effects seen in movies do not usually come from a non rotating black hole. They appear in scenes that show a rotating black hole, known as a Kerr black hole. The rotation causes the surrounding space to get pulled along, a phenomenon called frame dragging. This makes the time stretch much more than in the non rotating case. In many scenes the characters are also shown in a very fast orbit close to the event horizon. The combination of rotation, extreme gravity and high orbital speed creates time dilation that is far stronger than what a simple formula can represent.

This calculator focuses on the classic and easy to understand approach. It is ideal for learning the basic principles of gravitational time dilation.