The History of Calculators

Gabrielle Birchak/ May 23, 2024/ Ancient History, Modern History, Uncategorized

The year was 1983 and I was tak­ing the Scholas­tic Apti­tude Test, the SAT! It was spring­time in Den­ver, Col­orado, which meant it was snow­ing, as it usu­al­ly does until about June. I was prob­a­bly dressed in sweat­pants and leg warm­ers because, you know, the 80s. I remem­ber look­ing for­ward to the SAT test because I had been study­ing hard and was super pre­pared. I don’t remem­ber my exact scores. I didn’t do amaz­ing­ly well, but I didn’t do too bad­ly. I was a very aver­age stu­dent in high school. Clear­ly, I was sav­ing all my brain pow­er for col­lege. But I do remem­ber while tak­ing the test that I was long­ing for my FX-81 or even my EL-240H.

In case you’re won­der­ing what these let­ters and num­bers mean, they were the names of my trusty cal­cu­la­tors. My FX-81 was a Casio bat­tery-oper­at­ed sci­en­tif­ic cal­cu­la­tor, one of the three most excel­lent things in my back­pack. The oth­er two things were my Mat­tel elec­tron­ic hand­held foot­ball game and an I Heart New York cof­fee cup. I real­ly want­ed a Texas Instru­ment cal­cu­la­tor, but my par­ents couldn’t afford it. But I was pret­ty con­tent with the FX-81. It per­formed thir­ty sci­en­tif­ic func­tions and fac­to­ri­als and held up to six lev­els of paren­the­ses! I trea­sured that cal­cu­la­tor so much. I have always saved all of my cal­cu­la­tors, but for some rea­son, I’ve lost this one amidst forty years of mov­ing. But I still have my handy EL-240H, which was my very first cal­cu­la­tor. It was a solar-pow­ered Sharp cal­cu­la­tor that was giv­en to me by my broth­er John in 1978. Of course, being a the­ater stu­dent, I only pulled out my cal­cu­la­tors when I was alone and no one could see me. I didn’t want any­one to think that I was a total math nerd. Clear­ly, I’ve come out of the clos­et on that one.

So, speak­ing of cal­cu­la­tions, did you know that the tallest build­ing in the world, the Burj Khal­i­fa in Dubai, is as tall as 552 Dan­ny DeVi­tos, which is as tall as 14,529 donuts? It’s rather excit­ing to think that mea­sur­ing things in Dan­ny DeVi­tos or dough­nuts gives your per­spec­tive on cal­cu­lat­ing a new fun twist. Peo­ple have enjoyed cal­cu­lat­ing for thou­sands and thou­sands of years. There is proof of this etched in cuneiform tablets and writ­ten in papyrus. But once cal­cu­la­tors came along, they changed the whole process of com­put­ing num­bers in ways unimaginable.

As I note in my book, Hypa­tia, the Sum of Her Life, one of the very first math­e­mat­i­cal cal­cu­la­tors comes from an Aba­cus from 300 BC known as the Salamis Tablet, which was mar­ble with etch­ings of dots and lines. Users made cal­cu­la­tions by mov­ing the peb­bles between the lines. This antique tablet mea­sured 146 cen­time­ters by 57 cen­time­ters by 5 centimeters.

Around the same time, an aba­cus-like instru­ment called the Suan­pan was used in Chi­na. The Suan­pan held two decks of beads, with the upper deck hold­ing two beads and the low­er deck hold­ing five. It was a bi-quinary cod­ed sys­tem, much like our dec­i­mal sys­tem. The upper deck, designed with short rods, held two beads. The low­er deck, designed with longer rods, held five beads. The beads were count­ed by mov­ing them towards the beam.

By the fourth cen­tu­ry of our cur­rent era, Romans used a hand aba­cus made with met­al or bronze and had slots where the beads would sit. It wasn’t near­ly as advanced as the Suan­pan because no rods held the beads. Anoth­er com­mon one used in the fourth cen­tu­ry CE was the bi-quinary Aba­cus. The beads com­prised two-state (bi) and five-state (quinary) com­po­nents. This pock­et aba­cus allowed the Romans to use their estab­lished sys­tem for set­ting a place val­ue on frac­tions and dec­i­mals and exten­sive­ly large numbers.

In 1617, John Napi­er pre­sent­ed a man­u­al oper­a­tion for mul­ti­pli­ca­tion and divi­sion that includ­ed rods etched with val­ues rep­re­sent­ing a mul­ti­pli­ca­tion table. It used a process called lat­tice mul­ti­pli­ca­tion, which breaks up the dig­its that are mul­ti­plied into tables. It’s a won­der­ful con­cept that I will save for a lat­er pod­cast because I want to get to the good stuff about calculators.

In 1623, Wil­helm Schickard tried to cre­ate a mechan­i­cal cal­cu­lat­ing device that uti­lized Napi­er bones. But he aban­doned it a year lat­er. His notes showed it worked until he tried to prop­a­gate num­bers over, mean­ing adding one to 999. Upon doing so, it would jam the machine.

The first mechan­i­cal cal­cu­la­tor was pre­sent­ed in 1645 by Blaise Pas­cal, a French math­e­mati­cian. It was called the Pas­ca­line. This device was the result of fifty pro­to­types that he had cre­at­ed three years pri­or. This mechan­i­cal cal­cu­la­tor per­formed addi­tion and sub­trac­tion by turn­ing a dial that would move gears con­nect­ed to numer­i­cal wheels. One of its most valu­able fea­tures was that it had a car­ry mech­a­nism that would allow for adding one to nine on one dial, which would car­ry the one to the next dial when the first dial would change from a nine to a zero. They were expen­sive to make, which in turn made them expen­sive to sell. The Pas­ca­line was sold for around five hun­dred to six hun­dred livres, which was quite cost­ly in the sev­en­teenth cen­tu­ry. In today’s cur­ren­cy, five hun­dred to six hun­dred livres rough­ly equate to around ten to twelve thou­sand U.S. dol­lars. Pas­cal sold approx­i­mate­ly twen­ty of these Pascalines. 

Got­tfried Wil­helm Leib­niz, a Ger­man math­e­mati­cian and philoso­pher, made the sec­ond mechan­i­cal cal­cu­la­tor. Leib­niz pre­sent­ed his inven­tion to the Roy­al Soci­ety in Lon­don in 1673, called the Step Reck­on­er. He made only one Step Reck­on­er him­self. Still, he shared his designs and ideas, inspir­ing oth­ers to cre­ate their own Step Reck­on­ers. The Step Reck­on­er was not com­mer­cial­ly suc­cess­ful and wasn’t wide­ly sold.e third mechan­i­cal cal­cu­la­tor was made by Thomas de Col­mar, a French inven­tor, in the mid-nine­teenth cen­tu­ry. It was called the Arith­mome­ter. De Col­mar man­u­fac­tured around 5,000 Arith­mome­ters dur­ing his life­time, mak­ing it the first com­mer­cial­ly suc­cess­ful mechan­i­cal cal­cu­la­tor. The Arith­mome­ter was an improve­ment over the Pas­ca­line. It was more depend­able, faster, and capa­ble of per­form­ing more com­plex cal­cu­la­tions, such as mul­ti­pli­ca­tion and divi­sion, in addi­tion to addi­tion and subtraction.

The Arith­mome­ter per­formed mul­ti­pli­ca­tion through a series of mechan­i­cal oper­a­tions involv­ing the move­ment of gears and levers. It used a sys­tem of set­ting dials and cranks to input the num­bers to be mul­ti­plied and then mechan­i­cal­ly processed them to pro­duce the result. Around 5,000 Arith­mome­ters were man­u­fac­tured, and they were the most sold mechan­i­cal cal­cu­la­tor before the first dig­i­tal cal­cu­la­tor. The Arith­mome­ters were sold for around 300 to 600 francs, depend­ing on the mod­el and fea­tures, which was quite expen­sive at that time. Adjust­ed for infla­tion and con­sid­er­ing the pur­chas­ing pow­er, 300 to 600 francs back then would rough­ly equate to sev­er­al thou­sand U.S. dol­lars today.

Amer­i­can inven­tor Dorr Felt in 1882 designed one of our first and most suc­cess­ful mechan­i­cal cal­cu­la­tors, the Comp­tome­ter, was key-dri­ven. He built the first pro­to­type in 1884 using a mac­a­roni box, skew­ers, sta­ples, and rub­ber bands. It was patent­ed in 1887. It was used for almost 100 years, and its devel­op­ment was a pri­ma­ry foun­da­tion for devel­op­ing an elec­tron­ic calculator.

In 1902, our cal­cu­la­tors became small­er, but they still used the push but­ton mech­a­nism. The first one on the mar­ket was the Dal­ton Adding Machine. The orig­i­nal inven­tor was machin­ist Hubert Hop­kins. He and his broth­er William Hop­kins had been design­ing 10-key adding machines for over a decade. Hop­kins gave investor James Dal­ton the exclu­sive rights to man­u­fac­ture and sell this adding machine. In 1928, Rem­ing­ton Rand merged with Dal­ton and took over the sell­ing of the models.

In the ear­ly 1920s, Edith Clark, the first female elec­tri­cal engi­neer in the Unit­ed States, invent­ed the Clark Cal­cu­la­tor while work­ing for Gen­er­al Elec­tric. It was a graph­ing cal­cu­la­tor that solved line equa­tions using hyper­bol­ic func­tions, an elec­tric cur­rent, volt­age, and imped­ance in a pow­er trans­mis­sion line. Clarke was grant­ed her patent in 1925. 

Around 1948, portable cal­cu­la­tions were made pos­si­ble through the Cur­ta Cal­cu­la­tor, which is still used today. It’s a small cylin­der that fits in your hand and looks like a pep­per grinder. Its design was tak­en from the step reck­on­er and the Arith­mome­ter, which used val­ues on cogs. On the Cur­ta, there is a set of slides on the cylin­der part, with each slide rep­re­sent­ing a dig­it. The resul­tant counter sits at the top of the car­riage. When you input a num­ber and turn the crank, it adds anoth­er val­ue from the slides. This cylin­der allows for mul­ti­pli­ca­tion, divi­sion, addi­tion, and sub­trac­tion. It was a pop­u­lar device often used in the 1980s for sports car rallies. 

The first elec­tron­ic cal­cu­la­tor was invent­ed by Texas Instru­ments, an Amer­i­can tech­nol­o­gy com­pa­ny, in the ear­ly 1960s. It was called the Cal Tech and lat­er renamed the Pock­etron­ic. Its key fea­tures were that it was com­pact, portable, and pow­ered by bat­ter­ies. It per­formed basic func­tions like addi­tion, sub­trac­tion, mul­ti­pli­ca­tion, and divi­sion. It had a red light emit­ting diode (LED), which was top of the line at that time. It had mem­o­ry func­tions which allowed the user to store num­bers. And it was affordable.

The only prob­lem with it being called the Pock­etron­ic was that it didn’t fit into a pock­et unless you had a huge pock­et that was eight inch­es deep and four inch­es wide. In 1971, Busi­com mar­ket­ed their LE-120A Handy. This was con­sid­ered the first pock­et-size cal­cu­la­tor, pro­vid­ed that you had a pock­et that was five inch­es deep and three inch­es wide. That’s an odd size pock­et, but def­i­nite­ly small­er than the Pock­etron­ic. Regard­less, these cal­cu­la­tors pret­ty much only did basic mathematics.

But, stu­dents and engi­neers need­ed a sci­en­tif­ic cal­cu­la­tor capa­ble of per­form­ing a wide range of math­e­mat­i­cal func­tions, includ­ing trigonom­e­try, log­a­rithms, expo­nen­tials, and oth­er advanced func­tions. As a result, soon after the first hand­held elec­tron­ic cal­cu­la­tor, Hewlett-Packard intro­duced the HP-35 in 1972, the first sci­en­tif­ic cal­cu­la­tor. It was dis­con­tin­ued three years lat­er. This is like­ly because, at that point, cal­cu­la­tors were advanc­ing rather quick­ly. With­in the same decade, Hewlett-Packard pro­duced cal­cu­la­tors that could hold 100 instruc­tions, have con­tin­u­ous mem­o­ry, and retain pro­grams even after the cal­cu­la­tor had been turned off. Texas Instru­ments had intro­duced alge­bra­ic entries for sci­en­tif­ic nota­tion, a pi key, and log and trig functions.

The dis­play was also get­ting bet­ter. Rock­well Inter­na­tion­al began man­u­fac­tur­ing cal­cu­la­tors using liq­uid crys­tal dis­plays, also known as LCDs. These LCDs used dynam­ic scat­ter­ing mode, DSM, where the num­bers were bright against a dark back­ground. To cre­ate this con­trast, the LCD used a fil­a­ment lamp to make the num­bers stand out against the dark back­ground. Short­ly after this devel­op­ment, cal­cu­la­tors began to use twist­ed pneu­mat­ic LCDs, which placed dark num­bers against a light gray back­ground.
Final­ly, in the 1980s, many dis­trib­u­tors began cre­at­ing and sell­ing graph­ic cal­cu­la­tors. This was six­ty years after Edith Clarke’s first inven­tion of a graph­ic cal­cu­la­tor. For me, the 1980s were one of the great­est decades for cal­cu­la­tors. Music? That’s anoth­er sto­ry. I’ll go with the 90s on that one. How­ev­er, for cal­cu­la­tors, the 1980s was when the first graph­ing cal­cu­la­tor was sold. In 1985, Casio intro­duced the FX-7000G, which could dis­play bar graphs, line graphs, nor­mal dis­tri­b­u­tion curves, and regres­sion lines. What a time to be alive!

Today, graph­ic cal­cu­la­tors can plot equa­tions and func­tions on a coor­di­nate plane and han­dle three-dimen­sion­al graph­ics. With today’s graph­ic cal­cu­la­tors, we can visu­al­ize three-dimen­sion­al shapes and func­tions by rotat­ing them, zoom­ing in, and manip­u­lat­ing them. There are many of them on the mar­ket, includ­ing Texas Instrument’s TI-84 CE, the HP Prime Cal­cu­la­tor with a touch screen, and my favorite, the Casio Prizm FX-CG50. I like it because it cal­cu­lates faster, has the largest LCD size with col­or graph­ics, seems more user-friend­ly for pro­gram­ming, has a larg­er stor­age mem­o­ry, and offers a stripped-down Python envi­ron­ment. But I’ve been a devot­ed Casio girl since the 1990s, and buy­ing a cal­cu­la­tor is kind of like buy­ing under­wear. Every­body has their own per­son­al favorite. You just have to try them on to see what you like best.

As a side note, even though this pod­cast is about cal­cu­la­tors, there are some fan­tas­tic soft­ware and pro­grams that can do spe­cial­ized and advanced math­e­mat­ics, such as abstract alge­bra and sym­bol­ic manip­u­la­tion. These include Sage Math, Math­e­mat­i­ca, and Maple. All real­ly fan­tas­tic pro­grams.
There are a mul­ti­tude of cal­cu­la­tors avail­able today. 

As one who also loves cof­fee, the Caf­feine Informer has the Death-by-Caf­feine Cal­cu­la­tor so that you know how much not to drink. https://www.caffeineinformer.com/death-by-caffeine

The Unit­ed States Geo­log­i­cal Sur­vey Agency has a Drip Cal­cu­la­tor that can help you deter­mine how much water a leak­ing faucet wastes. https://water.usgs.gov/edu/activity-drip.html

The Glob­al Foot­print Net­work has the Foot­print Cal­cu­la­tor, which can tell you how many plan­ets it takes to sup­port your lifestyle. https://www.footprintcalculator.org/

At the Solar Sys­tems Col­li­sion Cal­cu­la­tor, you can pick your favorite plan­et and cal­cu­late what kind of aster­oid or comet you want to land on that plan­et and see what kind of dam­age it can do. Yes, it sounds a bit twist­ed. But some­thing tells me that if you’re lis­ten­ing to this, you are part of my tribe, and like me, you’re always down for some drink­ing and dri­ving on a Fri­day night with a Col­li­sion Cal­cu­la­tor? https://janus.astro.umd.edu/astro/impact/

If you want to dis­cov­er even more cal­cu­la­tors, vis­it the Omni­cal­cu­la­tor, which was designed by Physi­cist Steve Wood­ing, at https://www.omnicalculator.com, where you can find over 3,000 dif­fer­ent cal­cu­la­tors for a vari­ety of needs, includ­ing chem­istry, physics, food, health, and even weird units. And sup­pose you’re inter­est­ed in know­ing how many Dan­ny DeVi­tos it takes to get from your home to Booger Hole, West Vir­ginia, or how many dough­nuts it takes to cov­er the moon’s cir­cum­fer­ence. Well, the Omni­cal­cu­la­tor also has a Weird Units Con­vert­er, too, which can help you cal­cu­late var­i­ous mea­sure­ments, includ­ing Hol­ly­wood Signs, high heels, Eif­fel Tow­ers, slices of bread, or Lightsabers.

No doubt, cal­cu­la­tors are gen­uine­ly one of the great­est inven­tions ever made. We are mak­ing advance­ments in sci­ence and math­e­mat­ics along­side the prod­uct that is also mak­ing advance­ments in sci­ence and math­e­mat­ics. It’s fun when you think about it that way. Cal­cu­la­tors have made it an excit­ing time to study math­e­mat­ics, physics, chem­istry, and any endeav­or in sci­ence. And, even if the analy­sis gets tough, remem­ber that you can always count on your cal­cu­la­tor! (Pun intended)

I love cal­cu­la­tors. And if I have any cal­cu­la­tor addicts out there, please feel free to find me on social media or mes­sage me here and share with me your favorite calculator!

Thanks for vis­it­ing Math! Sci­ence! His­to­ry! Until next time, carpe diem!