The Richter Scale Equation and Earthquakes

The Richter scale formula is a measure of ground movement at the epicenter of an earthquake. This Richter scale number can then be used to calculate the energy released from an earthquake.

  • For example; the difference in power between the 8.8 magnitude earthquake in Chile and the 7.0 earthquake in Haiti is:  

The Chilean quake had 63 times as much ground movement

And released 501 times as much energy.

You can see how this is calculated at the bottom of this post, in the section called “Comparing the 8.8 magnitude quake in Chile to the 7.0 quake in Haiti”.

  • If you want to know how much power is represented by each order of magnitude of the Richter Scale, read the “What are the Energy Equivalents of different Earthquake Magnitudes?” section below.

 

  • If you want to calculate the difference in power between any two earthquakes then read the ‘Calculating the Increase in Magnitude’ section below.The Richter Scale Equation and Earthquakes

 

The bottom of this page has links to lists of recent earthquakes and earthquake maps.

 

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What are the Energy Equivalents of different Earthquake Magnitudes?    

  • Each order of magnitude releases around 31.6 times more energy than the previous magnitude. For example a magnitude 8.3 earthquake releases about 31.6 times more energy than a 7.3 magnitude quake.
  • The Richter Magnitude measurement of “0″ is set at a point where some energy is released. This was done in order to eliminate noise in the data.
Richter Magnitude  Amount of TNT Joule equivalent 
0 1 kg (2.2 lb) 4.2 MJ
1 32 kg (70 lb) 132.3 MJ
2 1 metric ton 4.18 GJ
3 31.6 metric tons 132.3 GJ
4 1 kiloton 4.18 TJ
5 31.6 kilotons 134.4 TJ
6 1 megaton 4.18 PJ
7 31.6 megatons 132.3 PJ
8 1 gigaton 4.18 EJ
9 31.6 gigatons 132.3 EJ
13 108 megatons 372.9 ZJ

     

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Calculating the Increase in Magnitude    

There are actually two ways to measure strength using the Richter Scale.    

  • First, there is the measurement of ground movement (which is measured by a seismometer).

  

  • Secondly there is the measurement of energy released. The measurement of the energy released is nearly directly correlated with ground movement.

 

  • Both of these measurements are for the epicenter of the quake.

 

  • The Richter Scale is a logarithmic scale and therefore each order of magnitude increase is a tenfold increase in the ground movement at the epicenter. A magnitude 2 quake causes 10 times more ground movement than a magnitude 1 quake (10^1=10).

 

  • However ground movement does not equal the energy released.

 

  • The energy released equals ground movement to the 1.5 power.

 

  • To determine the increase in ground movement and energy from two different earthquakes the following formulas are needed:    

Ground movement increase = 10^(increase in magnitude)

The increase in energy released = Ground movement increase^1.5

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(Note that this format won’t let me write exponents in the traditional way, so 4^2 means 4 squared).  

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So how does a magnitude 5 quake compare to a magnitude 2 earthquake?      

Well, the increase in magnitude is 5-2 or 3;  and 10^3 = 1000; thus the ground movement of a magnitude 5 quake is 1000 times greater than a magnitude 2 quake.    

And 1000^1.5 = 31,623; thus the energy released in a magnitude 5 quake is 31,623 times greater than a magnitude 2 quake.The Richter Scale Equation and Earthquakes    

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Comparing the 8.8 magnitude quake in Chile to the 7.0 quake in Haiti    

8.8 – 7.0 = 1.8 increase in magnitude.    

To determine the increase in movement use the formula 10^1.8 and you get 63.1 times more ground movement at the epicenter.    

But that number was for ground movement; the amount of energy released is a different number and is found by the equation 63.1^1.5 where you get 501 times as much energy released.    

So the Chilean earthquake caused 63 times more movement and released 501 times energy than the Haitian earthquake at the epicenter.    

 Now to add to the confusion; the epicenter of the Chilean quake was 22 miles below ground and the epicenter of the Haitian quake was 6 miles below ground.    

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As a side note; if you have Excel, you can add these formulas to any cell and it will give you the result. As an example, (=10^1.8^1.5) in Excel will give you 501. Make sure that you put in an equal sign first.

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Have there been any Earthquakes Today?

Here are some places where you can find an earthquake map or where you can find information about an earthquake today.

The USGS earthquake information.

Or a map of recent earthquakes.

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The following is from http://www.sdgs.usd.edu/ but updated by me.    

The Richter Scale Equation and Earthquakes    

*

Here is a list of famous earthquakes through history.

These quakes each killed over 50,000 people. This list of famous earthquakes can also be found at the USGS site.

The Richter Scale Equation and Earthquakes

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Lastly; will there be improvement in earthquake predictions?

According to one study; A large amount of sediment deposited over a tectonic plate might cause it to stick for a long time and then to jar loose with more damaging force.

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Please comment below if you have any questions, corrections, suggestions or clarifications.    

–*Also; Check out my post on ”The Mystery of Missing Matter” *–

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10 Responses to “The Richter Scale Equation and Earthquakes”

Read below or add a comment...

  1. Q says:

    Here’s a link saying the Chilean Quake Likely Shifted Earth’s Axis and the length of the day got shorter.
    http://www.bloomberg.com/apps/news?pid=newsarchive&sid=aLAUn4Gy92ss

  2. Robert Denby says:

    That’s an interesting link from bloomberg. Those were small changes, but it is fascinating to think that an earthquake can create permanent effects on the earth’s rotation.

  3. earthquake says:

    Earthquakes fascinate me. I found your information about earthquakes really interesting and I will be back to read more soon. Thanks.

  4. Mike Long says:

    It would be nice to see an update of this page for our Sept 4th, 2010 Earthquake in Christchurch (7.1). Especially noteworthy would be the number of deaths – zero.

  5. bjar says:

    hi
    I want Earthquake formula.
    please

  6. Boob says:

    cool info
    hi

  7. Sara says:

    To bjar
    E is proportional to ground movement to the power of 1.5
    Thanks for all the really good examples

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