The Mathematics of K = 0.73
How we calculate humanity's position on the Kardashev scale, with primary sources and exact formulas.
Stated Assumptions
This calculation makes the following explicit assumptions. Transparency about methodology is essential—no hand-waving.
Step-by-Step Workflow
Exactly how we transform raw energy data into a K-value. Every step is reproducible.
Scale Comparison
How our current position compares to higher civilization types on the logarithmic scale.
Origin of the Scale
Primary Source
Kardashev, N. S. (1964). "Transmission of Information by Extraterrestrial Civilizations." Soviet Astronomy, Vol. 8, No. 2, pp. 217-221.
Soviet astronomer Nikolai Kardashev proposed a classification scheme for civilizations based on their energy consumption while searching for extraterrestrial intelligence. He defined three discrete types based on observable energy signatures.
Sagan's Interpolation
Primary Source
Sagan, Carl (1973). The Cosmic Connection: An Extraterrestrial Perspective. Anchor Press/Doubleday. ISBN 978-0-521-78303-3.
Carl Sagan refined Kardashev's discrete scale into a continuous formula, allowing for intermediate values. This enables tracking incremental progress rather than waiting for discrete jumps between types.
The Formula
Where P is power consumption in watts, and K is the Kardashev value.
Why this formula? The logarithmic scale makes sense because energy consumption grows exponentially over time. A linear scale would make the jumps between types (1014 orders of magnitude) impossible to visualize. The formula yields K = 1.0 at 1016 W, K = 2.0 at 1026 W, and K = 3.0 at 1036 W.
Current Energy Consumption
Data Sources
- International Energy Agency (IEA) — World Energy Outlook 2023
- BP Statistical Review of World Energy 2023
- U.S. Energy Information Administration (EIA)
Conversion: 1 EJ/year ≈ 31.7 GW continuous. 604 EJ/year × 31.7 GW/(EJ/year) ≈ 19.1 TW. Conservative estimates range from 18-20 TW depending on methodology.
The Calculation
What This Means
0.73→ Current humanity
We harness about 0.007% of the energy reaching Earth from the Sun. We're a "Type 0.73" civilization—solidly sub-planetary.
1.0→ Type I (1016 W)
Complete utilization of Earth's incident solar radiation (~174 PW) and other planetary energy sources. Requires ~500× current consumption—achievable if energy production continues growing at ~2% annually for ~200 years.
2.0→ Type II (1026 W)
Harnessing the total energy output of a star (e.g., via a Dyson swarm). The Sun outputs ~3.8 × 1026 W. This represents a 10-billion-fold increase from Type I.
Historical Progression
Projections assume ~2-3% annual growth in energy production. Historical data from Vaclav Smil, "Energy Transitions: Global and National Perspectives" (2017).
Data Provenance
Direct links to verify our data sources. All claims are traceable to primary sources.
Primary Data Source
BP Statistical Review of World Energy 2024
Secondary Source
Our World in Data - Energy
How to Verify
- Download BP Statistical Review Excel workbook from the link above
- Navigate to "Primary Energy - Cons by fuel EJ" tab
- Find "Total World" row for the data year
- Convert EJ/year to TW: multiply by 31.7 GW/(EJ/year)
- Apply formula: K = (log10(P in watts) - 6) / 10
Academic References
[1] Kardashev, N. S. (1964)
"Transmission of Information by Extraterrestrial Civilizations." Soviet Astronomy, 8(2), 217-221.
ADS Abstract →[2] Sagan, Carl (1973)
The Cosmic Connection: An Extraterrestrial Perspective. Anchor Press/Doubleday. ISBN 978-0-521-78303-3.
Chapter 34: "Twenty Questions" contains the continuous scale interpolation formula.
[4] Smil, Vaclav (2017)
Energy Transitions: Global and National Perspectives. 2nd ed. Praeger. ISBN 978-1-4408-5324-1.
Comprehensive historical energy data from pre-industrial to present.