How to change the subject of a formula

February 17, 2013124 Comments

How to change the subject of a formula. A formula is a special equation which deals with ‘variables.’

Variables are bits of information that can change each time you deal with the formula.

For instance, one of the best known formulas is:

Speed = Distance / Time … and we use it every time we go somewhere.

If you’re driving at 30 miles per hour – the numbers can be put in place of the words:

Speed = Distance (30 miles) / Time (every 1 hour)


Speed = 30 miles / hour

Exam questions, that are based around this equation, usually ask you to work out one of the ‘terms.’ The questions are usually along the lines of:

  • How long does it take to travel 60 miles at a speed of 120 miles per hour?
  • How far have I travelled if I walk at 4mph for 3 hours?
They should be fairly straightforward to answer as
  • there are only three variables and
  • the three variables are all directly, or proportionately, related

Unfortunately it can be a little more difficult to change the subject (the first bit) to another part of the formula – particularly when there doesn’t seem to be a direct relationship.


Watch the videos and try the quick test.

Click here to try the Quick Test Rearranging Formula

Learning how to change the subject of a formula can be important depending upon what we are looking for; or different interpretations of the same thing. For instance in the UK we use degrees Centigrade to measure temperature, in America they use degrees Farenheit.

If you want to convert between Centigrade and Farenheit, both these formulas contain the same information – although each have different subjects:

tempconv2.png (357×128)


Follow these steps when learning how to change the subject of a formula:

  • Always work down the page with the equals sign in the middle
  • Deal with terms in the correct order (use BIDMAS: Brackets, Index (sometimes Order), Division and Multiplication together, Addition and Subtraction together
  • Always keep the formula in balance, write each side what you are doing
  • Don’t lose track of what you are trying to achieve!


Visit other related posts:
  • GCSE practice papers
  • How to solve linear equations with video examples
  • How to work with arithmetic sequences
  • Numeracy skills – how to work out percentages
  • How to add, subtract, multiply, divide decimals
  • Filed in: FoundationMaths Videos
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    Comments (124)

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    1. Brandon Saiger says:

      You genius. You legend. I’ll remember that for later exams

    2. ChickenElBito says:


    3. Atalaia Sol Lagos says:

      i love you u just saved my face froma detention thx

    4. CoolPlays says:

      The you just saved my neck!!!:)

    5. Joshua Dixon says:

      Hello Simon, I am having trouble with this question..
      Transpose the following equations, and solve by substitution:

      ”y = mx + c for m, and solve by substitution when y = 2, x = 3 and c =

      Any help would be appreciated. Thanks!

    6. Aman Marwaha says:

      Omg I have been looking everywhere for a clear cut tutorial like this thank
      you so much it really helped :)

    7. RedfernModelRailway says:

      Great Video! Despite being in top set maths, this has always been a topic
      that i have found difficult, your video helped clear up the points for me,
      although i think it is a little harder when the value on the top is not
      alone, e.g in your example it would be something like 8Q-3..

    8. Ben Duncan says:

      Excellent, thank you for that video.

    9. Daniel Follant says:

      Thanks so much i did not get it at all until your tutorial

    10. Luther Michalski says:

      It didn’t help

    11. Goldinfinityxi Pegauss says:

      everybody put the CAPTION english substitles LOOK WTF says really guys

    12. Epicnerd73 says:

      Thanks, this really helped :)

    13. Epicnerd73 says:

      Do you have any videos on solving difficult equations? I got this question
      in a past paper I was doing and I’ve got no idea where to start. Here is
      the question:
      Solve: 3/x -1 – 4/x+2 = 2
      The question is worth 7 marks and I don’t know how to do it. Could you help
      me or make a video on it? Thanks!

    14. cyriptobi137 says:

      Thanks for posting this is the clearest video on this topic!

    15. ruvindu saunya says:

      thank you very much. very usefull

    16. Roxy J says:

      I get the explanation above, but pls pls can somebody give me an step by
      step explanation of this equation:
      It would help with your learning too!
      I need to make *Y* the subject. *2y – 3x = 9*
      Thank you!

    17. Harry Norris says:

      Thank you so much, I couldn’t get this no matter what in my lessons, but
      something just clicked when I watched this. :)

    18. KrazeProductions says:

      I have a test tomorrow but thanks so much.I understand it now. i cant
      stress the ‘so’ much :)
      Earned another subscriber :)

    19. kashmala anwaar says:

      Thank you sooooo much!
      I was really struggling with this but you’ve made it a whole lot easier for
      me to do my test tomorrow!
      Thanks a million times

    20. Andrei Vaughn says:

      WAit wait i used this technique for a different question, I got to
      is the next step for me to divide both sides by x?
      which would leave me with yw+6 over x = x?

    21. CumWhore69 says:

      This guy is a lad
      What kind of heartless basterd can you be to dislike the video

    22. Birthday N says:

      You’re extremely helpful, I wouldn’t say I’m bad at maths in general, I’ve
      just always struggle with this!
      Thank you sir!

    23. Ali Alkuwari says:

      Thank you for the help I have test tomorrow :)

    24. jasdeep sandhu says:

      I HATE MATH!!!!!!

    25. Balla Abu says:

      pls help me with dis equation i have a test tomorrow x’2_26x+25=0

    26. Aslan Aslanli says:

      You helped me with this and now I am ready to do my math test

    27. eugene molley says:

      I’m kinda struggling with this algebra question and I’d be grateful if you
      could offer some assistance. how can I make B the subject of this formula:
      T=3(390s+90l+10b). Thank u.

    28. mancannon90k says:

      How do you do v X v= u X u + 2as, they don’t explain it

    29. Martin Jorgensen says:

      I have been reading text books and looking at web pages to try to figure
      out the correct process for changing the subject of a formula. I then
      clicked on a link to this video and I just got it… instantly! It all
      makes sense now thank you Simon.

    30. ali ghamyar says:

      z=(4 times( bracket v-2 all over 8) close bracket) 2 Simone can you please
      help me out with this? and is this a C grade or higher/ thanks
      and if you have more video of changing subject please let know

    31. ali ghamyar says:

      hi Simon.
      thanks for the video i was completely lost in the classroom by watching
      this video has actually open my mind

    32. Bangura Modoulamin says:


    33. NeronMC says:

      4:48 If “N” was 30, it would be 3,000(3 thousand) and not 30,000 thousand,

    34. hodgson1928 says:

      Great vid found this really helpful :)

    35. V Coates says:

      Hello, I understand what you have done. But you didn’t say why you did it
      in the order that you did. Are there specific rules to say that division,
      multiplication, subtraction, addition must be done in a certain order? For
      example, for the equation of a straight line… y=mx+c, I want to change
      the subject to ‘x’. If I subtract ‘c’ from both sides first I get y-c=mx,
      then I divide both sides by ‘m’, so I get y-c/m=x….however if I start by
      dividing both sides first I would get y/m=x+c and then I would subtract the
      ‘c’ from both sides, so I get y/m-c=x….so 2 different answers. I’m
      guessing there’s a rule I should be following, but I don’t know what it is?

    36. TheOrangedestruction says:

      Um how do you get the “minus 1″ from ? I mean the one in q( p – 1)

    37. Naynay Neo says:

      so… if i post my hw, will you do it for me? :D

    38. niraj bodalikar says:

      How do you make q the subject?

      P= q
      ——– + 2r
      Help please if you do see this can you show working out of how you did it

    39. Magdalena Garcia says:

      Wow! This was so helpful! Great video. Thank you!!!

    40. Sonal Hema Patel says:

      Struggled on this for ages! Thank God I clicked on your video! Awesome
      video! God bless you!

    41. Orient Express says:

      Thankyou :) You’re a life saver :)

    42. Greatsaiyanman says:

      so you dont have to work out the left hand side? you just show what you are
      doing to it. if anyone understands what i mean

    43. Tom Griff says:

      How would I change the subject to U in this formula? X=1/2 (u + v)t
      Thank you

    44. Oo Laitan says:

      I’ve just started Year 11 and I really want an A* in Maths! Hopefully
      watching your videos and practicing will help me get better :)

    45. Luke Voller says:

      What if the question is n= -3h+40. (Difference being its a minus)

    46. stephen barker says:

      when factorising is there a trick to knowing if its minus plus and they go

    47. stephen barker says:

      i need work out how rearrange formulae with 2 values the same

    48. RoxieRofl RozyRetzel says:

      Thank you so much !:D

    49. Samuel Cirdei says:

      Thanks a lot! Really helpful for tomorrow morning. Exam!

    50. jackster11997 says:

      Glad and faint for this video seen as my GCSE is Monday morning

    51. Wendy Mae says:

      Wish I had found your videos months ago…. my exam is Monday…. eeek..
      (and the last time I studied maths was 1987…..god help me!!)

    52. Sasha Mader says:

      I’m only in year 7 in Australia and this was really helpful!

    53. Etienne Purches says:

      Great video, this really helped me out (especially as I find this really
      tricky). I’ll admit I had to re-watch the video a couple of times mainly
      because I didn’t quite get it! Again great great video +1

    54. WolF_PaC.K says:

      How do you make a the subject if there’s brackets like M= (1+a) ₃

    55. miles barton-black says:

      How come you don’t minus q from the left hand side when you minus q from
      the right hand side

    56. genious razor says:

      Thanx alot it really helped me!!!!!!!

    57. MAJORSNODGRASS says:

      30 x 100 =3000 not 30000.

    58. Marisol Buitrago says:

      Great video! very useful! Thank you :)

    59. carla egea says:

      Thank u so so so much! My end of Year 10 exam is tomorrow and you really
      saved me! :):):)

    60. Jason Churches says:

      where can i find a more complicated question

    61. Toopsy Woopsy says:

      Man, it’s so much easier when it’s put into context and it’s in front of my
      eyes. I got an A in my mock exam and there was a question like this that I
      got wrong. Thanks for the help! + Earned a sub!

    62. Tashinga Matunga says:

      thanks ,you are a genius

    63. Claudia Pettifer says:

      This was useful.

    64. GHAZALA JABEEN says:

      This is great!!! Helped me a lot much appreciated

    65. Devil Spartan says:

      Thank you so much, i have an end of year test tomorrow and this helped a
      tonne :)

    66. freaker77 says:

      Thanks mate, taught it better than my lecturer :-)

    67. warsame abdi says:

      thank you so much

    68. joeymediauk says:

      Going in to an Earth sciences degree next year and have not studies maths
      since 2007 (My GCSEs) so I am relearning as much as I can before I begin.

      This actually really helped me figure this out

    69. muzhgan qaumi says:

      thank you so much this video was very helpful. i am at college doing higher
      level is there any anther video in higher level in youtube.
      thanks :)

    70. Joel Williams says:

      Once again great vid, thanks for the help!!!

    71. Joel Williams says:

      Thanks for the vid – has really helped me understand this topic in
      preparation for my end of year test!

    72. gibbo1112 says:

      When at the stage where you have PQ=Q+100P, my next steps were: (-Q)
      PQ-Q=100P then (/P) PQ-Q/P=100. Is this still correct?

    73. AM moses says:

      U r FAB!!!!! i tried all over the world trying to get this stuff in my head
      and finally now understand to due to YOU #THANKS SOOOOO MUCH!

    74. PROSNIPZ says:

      Thx so much I understand it now I have a end of term test next week.

    75. JezDayy says:

      I hate this question, I always get it wrong on the Grade B test. I got
      every question right except for this one because I wrote
      a=sqrt b² / c²

      instead of

      a=sqrt b² + c²

      and the question was

      “Rearrange the formula to make a the subject of a² – b² = c ²”

    76. JustAnother Uchiha says:

      thanks a lot for this , I got a GCSE mock next week , glad I finally
      understood this

    77. Shaun Taylor says:

      Thank You so much Saved my life!!!

    78. allmle75 says:

      Thanks your a life saver.

    79. Elisha Chouhan says:

      Thanks, this really helped me! i couldn’t understand my teacher but you
      took time and broke it down, taa . (:

    80. Tom Tra iner says:

      Im not sure if Im being stupid but at 4:50 did he say that 30×100 was

    81. Lo-Lo Haslam says:

      Thanks, helped alot!

    82. Kamran Ahmad says:

      thanks so much this really helped!

    83. Ali Almusawi says:

      Thanks a lot man :). You teach in a very simple and nice way. Keep it up!

    84. Kristina Herron says:

      Helped so much thanks!!

    85. methaloniangames says:

      Thanks great help I wont have to struggle with maths again now ive found
      your channel!!! :-)

    86. andrew jara says:

      helped so much thanks m8

    87. Ang Rui Yong says:

      Thanks for the help.

    88. Badders Bee says:

      Great help, cheers mate

    89. Olivia Mcgann says:

      I’m in year 9 and there’s so many people in my year i’ve been put into the
      highest year 10 group which is very hard and intimidating, this has helped
      me feel so much more confident thanksss

    90. Winnifred Barbara Parks says:

      Thanks,it is very helpfull

    91. SenurPenguin says:

      Thank you so very much!

    92. EBON1CS says:

      Absolute champion! You explained it slowly and thoroughly and all of a
      sudden it clicked! Thanks mate you’ve helped alot!

    93. TheMolovideos says:

      that helped so much i had homework on it.

    94. Simon Deacon says:

      Please like and leave a comment!

      Visit for real maths, tips and techniques.

    95. Jack Higgins says:

      Thanks this will help me loads with my revision for my GCSE
      mocks in January

    96. Alexander Combrink says:

      Wow this been very helpful! I am redoing my maths GCSE’s and my tutor
      hasn’t really explained this very well. Now I feel more knowledgeable

    97. Jazmin Chloe says:

      Hi, I’m in year 8 and this video explained everything to me! It was exactly
      what I needed for my exam preparation!

    98. Simon Deacon says:

      Thanks for the comment and all best with your studies :-)

    99. Dan McNab says:

      grateful for you and your videos, very relatable. thank you! brilliant for

    100. Simon Deacon says:

      Will do…I’ll let you know when posted. Rgds S

    101. SofaSwayKoala says:

      Hi, is there any possibility of requesting a video on Solving Quadratic equations? Thanks

    102. Simon Deacon says:

      Hi – there’s a couple of examples on Mathswrap . Visit maths help, look for quick tests and there’s one on rearranging formulas. Good luck !

    103. UrbanHDGamingVideo says:

      just wondering could you give an example of an A to A* question becausse i have an EXAM coming up and im doing A to A* so please reply so i have an idea of what’s coming up.

    104. Simon Deacon says:

      Hi – you’d need a bit more information to solve this. Maybe a way of finding values of some of the variables (x, m, n or p), or sometimes another equation that lets you work simultaneously. If you can post any more detail I’d be happy to help.

      All best


    105. HoldingCa says:

      Hey, I have a question, how would I go about solving x/m – x/n = 1/p

    106. Simon Deacon says:

      Please post, pin, tweet, like or subscribe!

    107. Simon Deacon says:

      Glad to help :-)

    108. Natho H says:

      Also, I have to say that you are a brilliant teacher, and I think that the fact that you are nice an slow makes what you say much easier to understand.

    109. Natho H says:

      Thanks you very much! This was really helpful for my homework.

    110. bzdurki3 says:

      Thank you

    111. Simon Deacon says:

      Hi Rebecca

      Bit of a difficult question, although you could say it as 100N-40 all over 3. The ‘all’ is important as you could misread your statement as 100N – 40/3. If you prefer to write it might be better to use brackets so:

      h = (100N – 40) over 3

      Hope this helps and thanks for the question.

      Kind Regards


    112. Rebecca Broughton says:

      hi im wondering if you can also write this as h=100N-40 over 3?

    113. SimoZXGaming says:

      Thanks so much, really helped. Good teacher you are, slow but surely explaining the solution. I’m confused on x = 5(a+b) [make b subject] at the moment, i’ll get it shortly though, thanks again

    114. navin kissoon says:


    115. mischigan taylor says:

      im in year 7 and ive got level 7?8 changing the formala

    116. Simon Deacon says:

      That’s great and thanks for your comment :-)

    117. Elmen Ortiz says:

      Thanks for the video. I will subscribe and hope to find more great Algebra videos.

    118. Cosmic Paudel says:

      Thank you it really helped

    119. Simon Deacon says:

      100N is the same as 3h + 40 – the main thing is to keep in balance. There’s some more info on MathsWrap – How to change the subject of a formula. Hope it helps and really pleased you’re having a go. All best S

    120. David Camel says:

      So 3h is the same as your explanation with 100N in the video!

    121. Simon Deacon says:

      Ah – that’s great – glad it helped. :-)

    122. David Camel says:

      Yes, thanks! I was thinking in your direction plus another. Did not want to get confused in my thinking.


    123. Simon Deacon says:

      Hi David – thanks for the question. The values of h and N can change – so 3h (which is 3 x h) could be any number times 3. If you divide both sides by 3 + 40 the 3 is ‘three times something’ and the 40 is ’40 added to something.’ Unfortunately they are completely separate ‘terms’ so you can’t treat them equally. Hope this helps? Kind Regards S

    124. David Camel says:

      Why cant h = 100N divided by 3+40 ? To make h the subject!

      100N = 3h + 40 can you not divide both sides by 3 + 40 ?

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