FINAL TOOLBOX
01 // Chart Studio02 // Visual Solvers03 // Calculators04 // Formulas05 // Unicode & Symbols
03 // Bidirectional STEM Calculators // PHYSICSΔt = Δt₀ / √(1 - β²)

Special Relativity Time Dilation Calculator

In Special Relativity, a clock moving at velocity fraction β = v / c relative to an inertial observer ticks slower by the Lorentz factor γ = 1 / √(1 - β²): Δt = Δt₀ / √(1 - β²).

Δt = Δt₀ / √(1 - β²)
Pick which value you want to calculate (or type into any field):Solving for: Δt — Dilated Observer Time
Calculated

Coordinate time elapsed for stationary observer

0.01100,000.00

Rest-frame time experienced onboard the moving craft

0.01100,000.00

Speed as a decimal fraction of light speed c (0 to 0.9999)

0.010.9999
unit
Calculated Result · Dilated Observer Time (Δt)
16.6667yr
Converted units:

Step-by-Step Calculation

01Canonical Law: Δt = Δt₀ / √(1 - β²)
02Given Inputs (Base Units): Δt₀ = 10 yr, β (v/c) = 0.8
03Solve for Δt (Dilated Observer Time): Δt = 16.6667 yr

In Special Relativity, a clock moving at velocity fraction β = v / c relative to an inertial observer ticks slower by the Lorentz factor γ = 1 / √(1 - β²): Δt = Δt₀ / √(1 - β²).

Real-World Reference Values

v = 0.80c (80% Light Speed)γ = 1.6667×

10 years onboard equals 16.67 years on Earth

v = 0.99c (99% Light Speed)γ = 7.0888×

1 year onboard equals 7.09 years on Earth

Cosmic Ray Muon (v = 0.9994c)γ = 28.87×

Allows short-lived upper-atmosphere muons to reach sea level

20-Row Comparison Table

Dilated Observer Time (Δt) · Proper Ship Time (Δt₀)

Special Relativity Time Dilation Calculator — Proper Ship Time → Dilated Observer Time
#Proper Ship Time (yr)Dilated Observer Time (yr)Δ %
0110 yrCurrent16.6667 yr0.00%
02724.2199 yr1,207.03 yr+7142.20%
031,448.43 yr2,414.05 yr+14384.30%
042,172.64 yr3,621.07 yr+21626.40%
052,896.85 yr4,828.08 yr+28868.50%
063,621.06 yr6,035.10 yr+36110.60%
074,345.27 yr7,242.12 yr+43352.70%
085,069.48 yr8,449.13 yr+50594.79%
095,793.69 yr9,656.15 yr+57836.89%
106,517.90 yr10,863.17 yr+65078.99%
117,242.11 yr12,070.18 yr+72321.09%
127,966.32 yr13,277.20 yr+79563.19%
138,690.53 yr14,484.22 yr+86805.29%
149,414.74 yr15,691.23 yr+94047.39%
1510,138.95 yr16,898.25 yr+101289.49%
1610,863.16 yr18,105.26 yr+108531.59%
1711,587.37 yr19,312.28 yr+115773.69%
1812,311.58 yr20,519.30 yr+123015.79%
1913,035.79 yr21,726.31 yr+130257.89%
2013,760.00 yr22,933.33 yr+137499.99%
Was this tool helpful?

Frequently Asked Questions

What is the Lorentz factor γ at β = 0.866?+

At β = √3 / 2 ≈ 0.866025 (86.6% of light speed), the Lorentz factor γ is exactly 2.0, so moving clocks run at half speed.

How fast must a spacecraft travel for 1 ship year to equal 10 Earth years?+

Click SOLVE FOR on β (v/c), set Δt = 10 and Δt₀ = 1. The required velocity is β = 0.994987c.

Does length contraction follow the same factor?+

Yes. Moving lengths contract along the axis of motion by the exact reciprocal factor: L = L₀ × √(1 - β²).