Units of Force, Energy, and Pressure:

A Working Scientist's Reference Table

Article By Global Instruments

Why These Three Quantities Cause the Most Confusion in Practice

Ask a room full of engineers, chemists, and physicists to state the SI unit of pressure, and most will answer correctly: the pascal. Ask them to convert a pressure reading from pounds per square inch to bar,

or a force reading from dynes to newtons, and the room grows quieter. Force, energy, and pressure are three of the most frequently used derived quantities in science and engineering, yet they are also three of the quantities most plagued by legacy units, regional conventions, and outdated textbooks that never fully made the transition to SI.

This is not a trivial housekeeping problem. Unit errors involving force, energy, and pressure have caused real damage — the loss of NASA's Mars Climate Orbiter in 1999 traced back to a mismatch between metric newton-seconds and imperial pound-seconds in navigation software is the most famous cautionary tale, but smaller, quieter unit-conversion mistakes happen daily in laboratories, pressure vessel design, structural engineering, and even clinical medicine, where blood pressure is still reported in millimeters of mercury rather than pascals. Understanding how these three quantities relate to each other, and how to move fluently between the unit systems still in active use, is a core competency for any working scientist or engineer.

This reference article lays out the modern SI framework for force, energy, and pressure, traces the older CGS and imperial units that persist in specific industries, and provides working conversion tables designed to sit next to a lab notebook or engineering workbook.

Force: The Foundation Quantity

Force is defined through Newton's second law of motion, F = ma, which directly ties the unit of force to the base units of mass, length, and time. In SI, the unit of force is the newton (N), named after Isaac Newton and adopted as a derived SI unit in 1948. One newton is defined as the force required to accelerate a one-kilogram mass at one meter per second squared:

1 N = 1 kg·m/s²

This clean definition is one of the underappreciated conveniences of SI — because force is built directly from the base units of kilogram, meter, and second, there is no separate conversion factor required within the system itself.

Outside SI, two other unit systems remain in active circulation. The CGS system (centimeter-gram-second), still used in some branches of physics and older scientific literature, defines force in dynes, where 1 dyne = 1 g·cm/s². The conversion is straightforward but easy to get wrong by orders of magnitude: 1 N = 100,000 dynes (10⁵ dyn).

The imperial/US customary system uses the pound-force (lbf), which is defined not from mass and acceleration directly but from the weight of a pound-mass under standard gravity (9.80665 m/s²). This distinction — between pound-mass and pound-force — is itself a frequent source of confusion, since the "pound" in everyday American usage conflates a unit of mass with a unit of force in a way that SI deliberately avoids. One pound-force equals approximately 4.44822 newtons.

A less common but historically important unit is the kilogram-force (kgf), sometimes called the kilopond, defined as the force exerted by standard gravity on one kilogram of mass. It appears in older European engineering drawings and some torque specifications, particularly in automotive and machine tool contexts. 1 kgf = 9.80665 N exactly, by definition.

Force Unit Conversion Table

From \ To	Newton (N)	Dyne	Pound-force (lbf)	Kilogram-force (kgf)
1 newton	1	100,000	0.224809	0.101972
1 dyne	0.00001	1	2.24809 × 10⁻⁶	1.01972 × 10⁻⁶
1 pound-force	4.44822	444,822	1	0.453592
1 kilogram-force	9.80665	980,665	2.20462	1

Energy: A Quantity With Too Many Historical Names

If force has three units in common use, energy has closer to a dozen, largely because energy shows up across so many distinct scientific traditions — mechanics, thermodynamics, electricity, nutrition, and atomic physics each developed their own preferred unit before SI unification efforts took hold.

The SI unit of energy is the joule (J), defined as the work done when a force of one newton acts over a displacement of one meter:

1 J = 1 N·m = 1 kg·m²/s²

The joule is elegantly consistent with the newton, which is itself elegantly consistent with the base units — this cascading consistency is one of the core design principles of the SI system, intended to eliminate the need for empirical conversion constants within a coherent unit system.

Despite this, several legacy energy units remain stubbornly persistent:

The calorie (cal), originally defined as the energy needed to raise one gram of water by one degree Celsius, remains standard in nutrition science (where it typically appears as the kilocalorie, confusingly often just labeled "Calorie" with a capital C) and in some areas of chemistry. 1 cal = 4.184 J (using the thermochemical calorie definition).

The erg, the CGS unit of energy, is defined as 1 g·cm²/s² and equals 10⁻⁷ joules — an inconveniently small unit for most macroscopic purposes, but still used in some areas of astrophysics and older physics literature.

The electronvolt (eV) is indispensable in atomic, nuclear, and particle physics, where energies at the scale of individual particles make the joule an impractically large unit. One electronvolt is the energy gained by an electron accelerating through a potential difference of one volt: 1 eV ≈ 1.602176634 × 10⁻¹⁹ J.

The British thermal unit (BTU), common in HVAC, power generation, and US industrial contexts, is defined as the energy required to raise one pound of water by one degree Fahrenheit. 1 BTU ≈ 1055.06 J.

The kilowatt-hour (kWh), used almost universally for electricity billing, is a unit of energy despite its name suggesting power; it represents the energy delivered by one kilowatt of power sustained for one hour. 1 kWh = 3,600,000 J (3.6 MJ).

Energy Unit Conversion Table

From \ To	Joule (J)	Calorie (cal)	Erg	Electronvolt (eV)	BTU	kWh
1 joule	1	0.239006	10,000,000	6.242 × 10¹⁸	0.000948	2.778 × 10⁻⁷
1 calorie	4.184	1	4.184 × 10⁷	2.611 × 10¹⁹	0.003966	1.162 × 10⁻⁶
1 erg	10⁻⁷	2.39 × 10⁻⁸	1	6.242 × 10¹¹	9.48 × 10⁻¹¹	2.778 × 10⁻¹⁴
1 BTU	1055.06	252.164	1.055 × 10¹⁰	6.585 × 10²¹	1	0.000293
1 kWh	3,600,000	860,421	3.6 × 10¹³	2.247 × 10²⁵	3412.14	1

Pressure: Where Legacy Units Refuse to Die

Pressure is defined as force distributed over an area, and its SI unit, the pascal (Pa), follows directly:

1 Pa = 1 N/m²

The pascal is a very small unit relative to everyday human-scale pressures — standard atmospheric pressure is roughly 101,325 Pa — which is part of the reason so many alternative pressure units remain in daily technical use even in countries that have otherwise adopted SI comprehensively.

The bar, widely used in meteorology, diving, and industrial process engineering, is defined as exactly 100,000 Pa, making it conveniently close to one standard atmosphere (1 bar ≈ 0.9869 atm). Its subunit, the millibar, remains standard in weather reporting, where it is increasingly labeled as the equivalent hectopascal (1 mbar = 1 hPa).

The atmosphere (atm), defined as exactly 101,325 Pa, represents standard sea-level atmospheric pressure and remains common in chemistry, particularly in gas law calculations and vapor pressure tables.

Pounds per square inch (psi), the dominant pressure unit in US industrial and automotive contexts (tire pressure, hydraulic systems, plumbing ratings), equals approximately 6894.76 Pa.

Millimeters of mercury (mmHg), also called torr (with a very slight historical distinction that is negligible for practical purposes), remains the standard unit in clinical blood pressure measurement and in vacuum technology. 1 mmHg ≈ 133.322 Pa.

Pressure Unit Conversion Table

From \ To	Pascal (Pa)	Bar	Atmosphere (atm)	psi	mmHg (torr)
1 pascal	1	0.00001	9.8692 × 10⁻⁶	0.000145	0.0075006
1 bar	100,000	1	0.98692	14.5038	750.062
1 atmosphere	101,325	1.01325	1	14.6959	760
1 psi	6894.76	0.068948	0.068046	1	51.7149
1 mmHg	133.322	0.00133322	0.00131579	0.0193368	1

Practical Guidance for Working Scientists

A few practical rules of thumb help avoid the most common unit-conversion errors in laboratory and engineering practice.

First, always identify whether a quoted "pound" is a unit of force or mass before doing any calculation involving weight, since this distinction is the single most common source of error when working between SI and US customary systems. In SI, mass and weight are never conflated; the kilogram is strictly a unit of mass, and weight is always expressed in newtons.

Second, when working with gas laws and thermodynamic calculations, be alert to which pressure and energy units a given source or instrument uses by default. Many older gas cylinders and regulators are calibrated in psi even in labs that otherwise report everything in SI, and calorimetry equipment sometimes reports directly in calories rather than joules.

Third, double-check unit consistency at both ends of any calculation, not just the final answer. A force in newtons multiplied by a distance in centimeters rather than meters will produce an answer that is off by a factor of 100 — small enough to look plausible, large enough to be dangerously wrong in a structural or pressure-vessel calculation.

Finally, when publishing or reporting scientific results, the International System of Units strongly recommends using SI units as the primary reported values, with legacy units given in parentheses only where an audience specifically expects them — for instance, reporting blood pressure in mmHg for a clinical audience alongside the SI-consistent kPa value for a broader scientific readership.

Conclusion

Force, energy, and pressure are quantities every scientist encounters daily, yet the coexistence of SI, CGS, and imperial conventions across different fields means that fluent, careful unit conversion remains a genuinely important working skill rather than a solved problem. The newton, joule, and pascal form an internally consistent, elegant foundation within SI, but the persistence of the dyne, calorie, BTU, psi, and mmHg across specific industries and disciplines means that a working reference table — of the kind provided above — remains an essential tool on any scientist's desk, not merely an academic exercise in unit history.

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