Before Calculators: How People Did the Maths by Hand
Published · 3 min read · By The Samsung Calculator editorial team
The problem they were solving
Multiplication by hand is slow and error-prone, and until the 1970s almost every quantitative profession depended on doing it thousands of times. Navigation, artillery, bridge design, insurance and astronomy all ran on multiplication of long decimals. The history of calculation is really the history of turning that multiplication into something easier.
Four technologies that did the job
The abacus, in use for at least 2,500 years, does not calculate — it stores. The operator performs the arithmetic mentally and the beads hold the intermediate state, which is exactly what human working memory runs out of. A trained abacus user still beats most people with a calculator on multi-digit addition.
Logarithm tables, published by John Napier in 1614, exploit the identity that log(a×b) = log(a) + log(b). Multiplication becomes look-up, addition, look-up — and a four-digit multiplication drops from minutes to seconds. Napier's tables took him twenty years to compute and reshaped astronomy within a decade.
The slide rule put those logarithms on sliding scales so the addition happened physically. It gives three significant figures and no decimal point, which means the user must always know the rough magnitude of the answer. Every Apollo engineer carried one. The habit it enforced — estimate first, compute second — disappeared with it.
Mechanical calculators began with Schickard's 1623 design and Pascal's 1642 Pascaline, which added and subtracted through geared wheels. Leibniz's stepped reckoner of 1694 added multiplication via a drum mechanism that survived in commercial machines into the 1970s. The Curta, a hand-cranked cylinder small enough for a pocket, was still being made in 1972 — four years after the first electronic pocket calculator.
Human computers
Before the word meant a machine, a computer was a person who computed. NACA and later NASA employed rooms of them; the Harvard Observatory ran on a team of women who catalogued hundreds of thousands of stars by hand. Katherine Johnson calculated orbital mechanics for Mercury and Apollo, and John Glenn famously asked her to verify by hand what the IBM 7090 had produced before he would fly.
The 1972 HP-35 changed this in about five years. It cost $395 — roughly $3,000 today — and did in one keystroke what a slide rule did in three with less precision. By 1975 slide rule production had essentially stopped, and the last major American maker closed its line.
What was lost
Slide rules forced estimation and gave three significant figures, which is honest for most engineering inputs. Calculators give ten, which invites false precision: a load estimate accurate to ±20% does not become better by being reported to eight decimal places. The discipline of knowing your input accuracy is the thing worth keeping from the pre-calculator era.
Worth trying
Estimate the answer before you type it. If you can get within 10% mentally, you will catch the misplaced decimal point that a calculator will happily hand you.
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About this article
Written and reviewed by The Samsung Calculator editorial team. Every calculator is written against a published formula, reviewed against at least one independent reference implementation, and dated when it changes. Last updated August 12, 2026. Spotted an error? Tell us.