How To Find Ka From PKa: Plus PKa To Ka & 4 Sample Problems

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Calculating Ka from pKa (and pKa from Ka) in Chemistry Download Article Explore this Article Sections 1 Calculating Ka from pKa 2 Calculating pKa from Ka 3 Can I find Ka (or pKa) without a calculator? 4 Sample Problems + Show 1 more... - Show less... Other Sections Video Related Articles Expert Interview References Co-authored by Anne Schmidt and Christopher M. Osborne, PhD

Last Updated: September 9, 2025 Fact Checked

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This article was co-authored by Anne Schmidt and by wikiHow staff writer, Christopher M. Osborne, PhD. Anne Schmidt is a Chemistry Instructor in Wisconsin. Anne has been teaching high school chemistry for over 20 years and is passionate about providing accessible and educational chemistry content. She has over 9,000 subscribers to her educational chemistry YouTube channel. She has presented at the American Association of Chemistry Teachers (AATC) and was an Adjunct General Chemistry Instructor at Northeast Wisconsin Technical College. Anne was published in the Journal of Chemical Education as a Co-Author, has an article in ChemEdX, and has presented twice and was published with the AACT. Anne has a BS in Chemistry from the University of Wisconsin, Oshkosh, and an MA in Secondary Education and Teaching from Viterbo University. This article has been fact-checked, ensuring the accuracy of any cited facts and confirming the authority of its sources. This article has been viewed 30,682 times.

Ka ( K a {\displaystyle K_{a}} )—the acid dissociation constant—tells you the strength of an acid in a different and more specific way than the better-known pH.[1] Because Ka produces extremely wide-ranging values, pKa ( p K a {\displaystyle pK_{a}} )—the negative logarithm (base 10) of Ka—is often used to simplify the range of acid strength values. If all of this is twisting your brain a little, here’s some good news: it’s actually pretty easy to figure out Ka from pKa (or pKa from Ka) with a scientific calculator, or to get a decent estimate without a calculator.[2] And we’ll show you how to do it all!

Things You Should Know

• Calculate Ka from pKa with the equation K a = 10 − p K a {\displaystyle Ka=10^{-pKa}} .
• Calculate pKa from Ka with the equation p K a = − l o g ( K a ) {\displaystyle pKa=-log(Ka)} .
• Estimate pKa from Ka (or vice versa) based on the pseudo-equation n ∗ 10 − m = ( m − 1 ) . ( 10 − n ) {\displaystyle n*10^{-m}=(m-1).(10-n)} .

Steps

Section 1 of 4:

Calculating Ka from pKa

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1. 1 Use the equation K a = 10 − p K a {\displaystyle Ka=10^{-pKa}} for this conversion. pKa is defined as the negative logarithm (-log) of Ka, which means you calculate pKa with the calculation p K a = − l o g ( K a ) {\displaystyle pKa=-log(Ka)} . Solving instead for Ka requires you to raise both sides of the equation by exponents of 10:[3]
   • 10 p K a = 10 − l o g ( K a ) {\displaystyle 10^{pKa}=10^{-log(Ka)}}
   • 10 − p K a = 10 l o g ( K a ) {\displaystyle 10^{-pKa}=10^{log(Ka)}}
   • 10 − p K a = K a {\displaystyle 10^{-pKa}=Ka} → K a = 10 − p k a {\displaystyle Ka=10^{-pka}}
   • For this example, we’ll say p K a = 14 {\displaystyle pKa=14} (which is in fact the pKa for plain water).
2. 2 Enter the right side of the equation in your scientific calculator. Using a scientific calculator varies a bit by model and type (for both online and physical calculators), but the buttons are generally similar.[4] For this article, we’ll use the online scientific calculator that appears when you Google “scientific calculator.”
   • Type in 10 {\displaystyle 10} .
   • Press the x y {\displaystyle x^{y}} button.
   • Type − 14 {\displaystyle -14} in the superscript box.
   • Press the = {\displaystyle =} button.
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3. 3 Translate the answer 1 e − 14 {\displaystyle 1e-14} . The result you get may not appear in the format you expect, but it is the right answer. Simply substitute ∗ 10 {\displaystyle *10} for e {\displaystyle e} and raise − 14 {\displaystyle -14} to superscript:
   • 1 e − 14 {\displaystyle 1e-14} equals 1 ∗ 10 − 14 {\displaystyle 1*10^{-14}} .
   • So a pKa of 14 {\displaystyle 14} equals a Ka of 1 ∗ 10 − 14 {\displaystyle 1*10^{-14}} .
   • In some cases, your calculator may provide the answer in decimal form, such as K a = 0.00072 {\displaystyle Ka=0.00072} instead of its equivalent K a = 7.2 ∗ 10 − 4 {\displaystyle Ka=7.2*10^{-4}} . The latter format is typically how Ka is represented, however.
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Section 2 of 4:

Calculating pKa from Ka

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1. 1 Do this conversion with the equation p K a = − l o g ( K a ) {\displaystyle pKa=-log(Ka)} . pKa exists largely as a matter of convenience, since the Ka of acids are unwieldy values like 1.54 ∗ 10 − 2 {\displaystyle 1.54*10^{-2}} and 1.34 ∗ 10 − 5 {\displaystyle 1.34*10^{-5}} . However, converting to the negative logarithm (-log) of these values creates much more manageable figures like 1.81 {\displaystyle 1.81} and 4.87 {\displaystyle 4.87} .
   • Converting to the -log means that a lower pKa value indicates a stronger acid, as opposed to the Ka, in which a higher Ka value indicates a stronger acid.
   • In this example, let’s make K a = 4 ∗ 10 − 4 {\displaystyle Ka=4*10^{-4}} (nitrous acid).
2. 2 Input the right side of the equation in a scientific calculator. As with our pKa to Ka conversion, we’ll assume you’re using Google search’s scientific calculator:
   • Press the − {\displaystyle -} button.
   • Press the l o g {\displaystyle log} button.
   • Enter 4 ∗ 10 {\displaystyle 4*10} inside the parentheses.
   • Press the x y {\displaystyle x^{y}} button.
   • Enter − 4 {\displaystyle -4} in the superscript box.
   • Press the = {\displaystyle =} button.
3. 3 Confirm your answer. For the example − l o g ( 4 ∗ 10 − 4 ) {\displaystyle -log(4*10^{-4})} , your answer should be 3.4 {\displaystyle 3.4} . So in this case p K a = 3.4 {\displaystyle pKa=3.4} .
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Section 3 of 4:

Can I find Ka (or pKa) without a calculator?

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1. You can get a quick estimate that may help on a multiple-choice exam. The trick is to use the “equation”[5] n ∗ 10 − m = ( m − 1 ) . ( 10 − n ) {\displaystyle n*10^{-m}=(m-1).(10-n)} :
   • Finding an estimate of pKa from Ka is easier. Say, for example, Ka equals 2.33 ∗ 10 − 11 {\displaystyle 2.33*10^{-11}} :
     • Based on this Ka and the “equation” given above, n = 2.33 {\displaystyle n=2.33} and m = 11 {\displaystyle m=11} . Round n {\displaystyle n} to a single digit if needed (2 in this case), then plug these into the second half of the “equation.”
     • ( 11 − 1 ) . ( 10 − 2 ) {\displaystyle (11-1).(10-2)} → 10.8 {\displaystyle 10.8} .
     • Your estimate of Ka is 10.8, while the actual answer is 10.63.
   • Estimating Ka from pKa (let’s say it equals 10.63) is a bit trickier and less accurate:
     • Round to a single digit after the decimal as needed: 10.63 → 10.7
     • Based on the ( m − 1 ) . ( 10 − n ) {\displaystyle (m-1).(10-n)} half of the “equation,” add 1 to the 10 (from 10.7) to get m {\displaystyle m} and subtract the 7 (from 10.7) from 10 to get n {\displaystyle n} ; so m = 11 {\displaystyle m=11} and n = 3 {\displaystyle n=3} .
     • Plug the results (m=11 & n=3) into the first half of the “equation”: 3 ∗ 10 − 11 {\displaystyle 3*10^{-11}} is your estimate for Ka, while the actual answer is 2.33 ∗ 10 − 11 {\displaystyle 2.33*10^{-11}} .

Section 4 of 4:

Sample Problems

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1. 1 What is Ka if pKa equals 3.14?
   • K a = 10 − p K a {\displaystyle Ka=10^{-pKa}}
   • K a = 10 − 3.14 {\displaystyle Ka=10^{-3.14}}
   • K a = 0.00072 {\displaystyle Ka=0.00072} → K a = 7.2 ∗ 10 − 4 {\displaystyle Ka=7.2*10^{-4}}
2. 2 What is Ka if pKa equals 11.62?
   • K a = 10 − p K a {\displaystyle Ka=10^{-pKa}}
   • K a = 10 − 11.65 {\displaystyle Ka=10^{-11.65}}
   • K a = 2.2 e − 12 {\displaystyle Ka=2.2e^{-12}} → K a = 2.2 ∗ 10 − 12 {\displaystyle Ka=2.2*10^{-12}} [6]
3. 3 What is pKa if Ka equals 2.33 ∗ 10 − 11 {\displaystyle 2.33*10^{-11}} ?
   • p K a = − l o g ( K a ) {\displaystyle pKa=-log(Ka)}
   • p K a = − l o g ( 2.33 ∗ 10 − 11 ) {\displaystyle pKa=-log(2.33*10^{-11})}
   • p K a = 10.63 {\displaystyle pKa=10.63} [7]
4. 4 What is pKa if Ka equals 6.46 ∗ 10 − 5 {\displaystyle 6.46*10^{-5}} ?
   • p K a = − l o g ( K a ) {\displaystyle pKa=-log(Ka)}
   • p K a = − l o g ( 6.46 ∗ 10 − 5 ) {\displaystyle pKa=-log(6.46*10^{-5})}
   • p K a = 4.19 {\displaystyle pKa=4.19}
5. 5 Estimate pKa if Ka equals 5.6 ∗ 10 − 10 {\displaystyle 5.6*10^{-10}} .
   • Using n ∗ 10 − m = ( m − 1 ) . ( 10 − n ) {\displaystyle n*10^{-m}=(m-1).(10-n)} , plug 5 (from 5.6) in as n {\displaystyle n} and 6 (from 5.6) in as m {\displaystyle m} in the second half of the “equation.”[8]
   • (10-1).(10-6) → 9.4. The accurate result for PKa is 9.25.
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Expert Interview

Thanks for reading our article! If you’d like to learn more about chemistry, check out our in-depth interview with Anne Schmidt.

References

1. ↑ Anne Schmidt. Chemistry Instructor. Expert Interview
2. ↑ https://study.com/skill/learn/how-to-convert-between-ka-and-pka-explanation.html
3. ↑ http://www.csun.edu/~jm77307/pH%20and%20Buffers.pdf
4. ↑ https://study.com/skill/learn/how-to-convert-between-ka-and-pka-explanation.html
5. ↑ https://study.com/skill/learn/how-to-convert-between-ka-and-pka-explanation.html
6. ↑ http://www.csun.edu/~hcchm003/321/Ka.pdf
7. ↑ http://www.csun.edu/~hcchm003/321/Ka.pdf
8. ↑ https://study.com/skill/learn/how-to-convert-between-ka-and-pka-explanation.html

About This Article

Co-authored by: Anne Schmidt Chemistry Instructor This article was co-authored by Anne Schmidt and by wikiHow staff writer, Christopher M. Osborne, PhD. Anne Schmidt is a Chemistry Instructor in Wisconsin. Anne has been teaching high school chemistry for over 20 years and is passionate about providing accessible and educational chemistry content. She has over 9,000 subscribers to her educational chemistry YouTube channel. She has presented at the American Association of Chemistry Teachers (AATC) and was an Adjunct General Chemistry Instructor at Northeast Wisconsin Technical College. Anne was published in the Journal of Chemical Education as a Co-Author, has an article in ChemEdX, and has presented twice and was published with the AACT. Anne has a BS in Chemistry from the University of Wisconsin, Oshkosh, and an MA in Secondary Education and Teaching from Viterbo University. This article has been viewed 30,682 times. 6 votes - 100% Co-authors: 10 Updated: September 9, 2025 Views: 30,682 Categories: Chemistry In other languages Spanish Portuguese

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Yes No Advertisement If you buy through links on our site, we may earn a commission.Cookies make wikiHow better. By continuing to use our site, you agree to our cookie policy. Co-authored by: Anne Schmidt Chemistry Instructor Co-authors: 10 Updated: September 9, 2025 Views: 30,682 100% of readers found this article helpful. 6 votes - 100% Click a star to add your vote

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