Richter Scale to Moment Conversion Calculator
Our geology & geophysics calculator computes richter scale moment conversion accurately. Enter measurements for results with formulas and error analysis.
Formula
Mw = 0.67 ML + 2.07 (ML > 6) | Mw = 0.99 Ms + 0.08 (Ms > 6.1)
Empirical relationships from Scordilis (2006) convert between magnitude scales. For small earthquakes (ML < 6), Mw is approximately equal to ML. For larger events, regression equations account for ML saturation. Surface wave magnitude Ms converts to Mw using a separate regression.
Worked Examples
Example 1: ML to Mw for Large Earthquake
Problem: A seismograph records ML = 7.2. Estimate the moment magnitude.
Solution: For ML > 6.0: Mw = 0.67 x 7.2 + 2.07 = 4.824 + 2.07 = 6.89\nM0 = 10^(1.5 x 6.89 + 9.1) = 10^19.435 = 2.72e19 N\u00B7m
Result: Mw = 6.89 (ML saturates, actual earthquake is smaller in Mw)
Example 2: Ms to Mw Conversion
Problem: A teleseismic earthquake has Ms = 7.8. Find Mw.
Solution: For Ms > 6.1: Mw = 0.99 x 7.8 + 0.08 = 7.722 + 0.08 = 7.80
Result: Mw = 7.80 (Ms and Mw agree well at this range)
Frequently Asked Questions
Why did scientists move from the Richter scale to moment magnitude?
The Richter scale (local magnitude ML) was developed in 1935 by Charles Richter for Southern California earthquakes and measures the maximum amplitude on a Wood-Anderson seismograph. It saturates around magnitude 7, meaning it cannot properly distinguish between very large earthquakes. Moment magnitude (Mw) was introduced in 1979 by Hanks and Kanamori and is based on the total seismic energy released, making it reliable for all earthquake sizes without saturation.
Are Richter and moment magnitude values the same for small earthquakes?
For earthquakes below about magnitude 6, the Richter scale (ML) and moment magnitude (Mw) give very similar values, typically within 0.1-0.3 units of each other. This is by design, as the Mw scale was calibrated to match ML in this range. The scales diverge significantly for large earthquakes above magnitude 6.5, where the Richter scale underestimates the true size because the measured wave amplitude saturates.
What are the most common unit conversion mistakes?
Common errors include confusing fluid ounces with weight ounces, mixing up miles and nautical miles, forgetting that UK and US gallons differ (UK is 20% larger), using the wrong temperature formula, and not accounting for the difference between troy and avoirdupois ounces.
How accurate are the results from Richter Scale to Moment Conversion Calculator?
All calculations use established mathematical formulas and are performed with high-precision arithmetic. Results are accurate to the precision shown. For critical decisions in finance, medicine, or engineering, always verify results with a qualified professional.
Can I use Richter Scale to Moment Conversion Calculator on a mobile device?
Yes. All calculators on NovaCalculator are fully responsive and work on smartphones, tablets, and desktops. The layout adapts automatically to your screen size.
Is my data stored or sent to a server?
No. All calculations run entirely in your browser using JavaScript. No data you enter is ever transmitted to any server or stored anywhere. Your inputs remain completely private.