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Richter Scale Practice Problems

Earthquake problems come in four types: find a magnitude, compare shaking, compare energy, or work backwards from a ratio. Each one is a single step with a common logarithm or a power of ten once you know which formula to reach for.

  1. 1.

    A seismograph records waves 1,000 times the reference amplitude . What is the magnitude?

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    , because .

  2. 2.

    How many times larger is the wave amplitude of a magnitude 5 earthquake than a magnitude 3?

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    The difference is 2, so the ratio is .

  3. 3.

    An earthquake's waves are 1,000,000 times the reference amplitude. What is its magnitude?

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    , because .

  4. 4.

    By what factor does the energy released grow for each increase of 1 in magnitude? Give one decimal place.

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    Energy grows by per step, much faster than the growth in shaking.

  5. 5.

    An earthquake's waves are 4,500 times the reference amplitude. Find its magnitude to two decimal places.

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    .

  6. 6.

    How many times larger is the wave amplitude of a magnitude 6.8 earthquake than a magnitude 5.3? Give two decimal places.

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    The difference is , so the ratio is .

  7. 7.

    How many times more energy does a magnitude 7 earthquake release than a magnitude 5?

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    .

  8. 8.

    A magnitude 4.6 earthquake has waves how many times the reference amplitude? Round to the nearest whole number.

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    Rewrite in exponential form: .

  9. 9.

    An earthquake produces waves 80 times the amplitude of a magnitude 3.9 quake. What is its magnitude, to two decimal places?

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    The ratio gives the difference: . So .

  10. 10.

    How many times more energy did a magnitude 9.1 earthquake release than a magnitude 7.8? Give one decimal place.

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    The difference is , so the energy ratio is .

  11. 11.

    An earthquake releases 1,000 times the energy of a magnitude 5.4 earthquake. What is its magnitude?

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    , so and . The magnitude is .

  12. 12.

    One earthquake releases 500 times the energy of another. What is the difference in their magnitudes, to two decimal places?

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    , so and .
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Richter Scale Practice Problems

These problems follow the Richter scale lesson. If converting between log form and exponential form is new, start with the logarithms lesson.

The formulas you need

QuestionFormula
magnitude from amplitude
amplitude from magnitude
how many times the shaking
how many times the energy

Before you calculate

Use the base-10 key, not . Subtract the magnitudes first, then raise to that difference. Never subtract amplitudes or energies directly.

Common mistakes to watch for

  • Treating the scale as linear. Each whole number up means 10 times the amplitude.
  • Confusing amplitude with energy. Each step is about 31.6 times the energy, not 10 times.
  • Subtracting amplitudes. Compare by the difference in magnitudes: .
  • Rounding too early. Keep full precision until the final answer.

Frequently Asked Questions

Which formula do I use for comparing two earthquakes?+

For shaking or wave amplitude, use 10^(M₁ − M₂). For energy, use 10^(1.5(M₁ − M₂)). The question's wording, 'amplitude' or 'energy', tells you which.

How do I find a magnitude from an amplitude?+

Divide the amplitude by the reference amplitude A₀ and take the common log: M = log(A / A₀). If the problem already gives the ratio, just take its log.

Do I use log or ln for Richter scale problems?+

Always the common log, base 10. The Richter scale is defined in powers of ten.

How should I enter my answers?+

Type numbers without commas, for example 39811, and round to the place the question asks for. Answers within that rounding are marked correct.

More practice problems

Logarithm Practice Problems Common and Natural Log Practice Problems Exponential and Logarithmic Functions Practice Problems