Gravitational Time Dilation Calculator
Calculate how gravity affects the passage of time using Einstein's general theory of relativity
Mass of the gravitational object (e.g., Earth ≈ 5.972 × 10²⁴ kg)
Distance from the center of the mass (e.g., Earth's radius ≈ 6,371,000 m)
How to Use This Calculator
Enter the Mass
Input the mass of the gravitational object in kilograms. For Earth, use approximately 5.972 × 10²⁴ kg.
Enter the Distance
Input the distance from the center of the mass in meters. For Earth's surface, use approximately 6,371,000 m.
Calculate
Click "Calculate Time Dilation" to get the time dilation factor and time differences.
Interpret Results
The time dilation factor shows how much slower time runs compared to infinity. A value close to 1 means minimal dilation, while smaller values indicate significant time dilation.
Formula
Time Dilation Factor: t' / t = √(1 - rₛ/r)
Schwarzschild Radius: rₛ = 2GM/c²
where G is gravitational constant, M is mass, c is speed of light, r is distance from center
Example 1: Earth's Surface
Given: Mass = 5.972 × 10²⁴ kg, Radius = 6,371,000 m
rₛ = 2 × 6.674 × 10⁻¹¹ × 5.972 × 10²⁴ / (299,792,458)²
rₛ = 8.87 × 10⁻³ m (8.87 mm)
Time dilation factor = √(1 - 8.87 × 10⁻³ / 6,371,000) = 0.9999999993
Time runs slower by about 6.95 × 10⁻¹⁰ per second
This is about 0.022 seconds per year slower than at infinity
Example 2: Near a Black Hole
Given: Mass = 1 × 10³¹ kg (5 solar masses), Radius = 1.5 × 10⁷ m
rₛ = 2 × 6.674 × 10⁻¹¹ × 1 × 10³¹ / (299,792,458)²
rₛ = 1.48 × 10⁷ m
Time dilation factor = √(1 - 1.48 × 10⁷ / 1.5 × 10⁷) = 0.115
Time runs 8.7 times slower than at infinity!
About Gravitational Time Dilation
Gravitational time dilation is a phenomenon predicted by Einstein's general theory of relativity. It states that time runs slower in stronger gravitational fields. This effect has been confirmed by numerous experiments and is essential for GPS satellites, which must account for both gravitational and velocity time dilation to maintain accuracy.
How Gravity Affects Time
According to general relativity, gravity is the curvature of spacetime caused by mass. This curvature affects not only the paths of objects but also the flow of time itself. Clocks run slower in stronger gravitational fields, meaning time passes more slowly near massive objects.
When to Use This Calculator
- Physics Education: Teaching students about general relativity and time dilation
- GPS Systems: Understanding why GPS satellites need time corrections
- Astrophysics: Calculating time dilation near stars, black holes, and neutron stars
- Research: Analyzing gravitational effects in theoretical and experimental physics
- Science Communication: Explaining relativity to general audiences
Why Use Our Calculator?
- ✅ Instant Results: Calculate gravitational time dilation immediately
- ✅ Accurate: Uses precise formulas from general relativity
- ✅ Educational: Clear explanations and worked examples
- ✅ 100% Free: No registration or payment required
- ✅ Practical: Shows time differences per year for real-world perspective
- ✅ Comprehensive: Calculates Schwarzschild radius and time dilation factor
Real-World Applications
GPS Satellites: GPS satellites orbit at about 20,000 km altitude, where gravity is weaker than on Earth's surface. However, they also move fast, experiencing velocity time dilation. The net effect is that GPS clocks run faster by about 38 microseconds per day, which must be corrected for accurate positioning.
Black Holes: Near a black hole's event horizon (Schwarzschild radius), time dilation becomes extreme. From a distant observer's perspective, time appears to stop at the event horizon, making it impossible to see objects cross it.
Pulsars and Neutron Stars: These extremely dense objects have strong gravitational fields, causing measurable time dilation effects that can be observed in their signals.
Tips for Best Results
- For Earth, the time dilation effect is very small but measurable
- Time dilation becomes significant near black holes and neutron stars
- The Schwarzschild radius must be less than the distance to avoid the event horizon
- Time dilation factor approaches 1 for weak gravitational fields
- Time dilation factor approaches 0 near the event horizon of a black hole
Frequently Asked Questions
What is gravitational time dilation?
Gravitational time dilation is the effect where time runs slower in stronger gravitational fields. This is predicted by Einstein's general theory of relativity and has been confirmed by experiments.
How does this differ from velocity time dilation?
Velocity time dilation (from special relativity) occurs when objects move at high speeds. Gravitational time dilation (from general relativity) occurs due to gravity. Both effects can occur simultaneously, as in GPS satellites.
Why do GPS satellites need time corrections?
GPS satellites experience both effects: they move fast (velocity time dilation makes clocks run slower) and are in weaker gravity (gravitational time dilation makes clocks run faster). The net effect is that GPS clocks run faster by about 38 microseconds per day, requiring correction.
What is the Schwarzschild radius?
The Schwarzschild radius is the radius at which the escape velocity equals the speed of light. For a mass, it's calculated as rₛ = 2GM/c². If an object is compressed to within this radius, it becomes a black hole.
Can time stop completely?
From a distant observer's perspective, time appears to stop at the event horizon of a black hole. However, an observer falling into a black hole would experience time normally from their perspective. This is a key feature of general relativity.
Is gravitational time dilation measurable on Earth?
Yes! Modern atomic clocks are precise enough to measure the time difference between different altitudes on Earth. Clocks run slightly faster at higher altitudes where gravity is weaker. This was confirmed by experiments in the 1970s.