Calculate pressure using P=F/A. Convert between Pascals, bar, psi, atm, and mmHg. Covers atmospheric pressure, blood pressure, fluid pressure, and Boyle's Law.
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Pressure is the force applied per unit area. The greater the force or the smaller the area, the higher the pressure.
Worked Example: A force of 200 N acts on an area of 0.04 m². Pressure = 200 ÷ 0.04 = 5,000 Pa (5 kPa).
Why small areas create high pressure: A stiletto heel (area ≈ 1 cm² = 0.0001 m²) supporting 600 N of body weight creates a pressure of 600 ÷ 0.0001 = 6,000,000 Pa (6 MPa) — enough to damage floors.
One atmosphere (1 atm) is the internationally recognised reference pressure, equal to the average air pressure at sea level.
| Unit | Symbol | Value in Pa | Equivalent |
|---|---|---|---|
| Pascal | Pa | 1 Pa | 1 N/m² |
| Kilopascal | kPa | 1,000 Pa | 0.01 bar |
| Bar | bar | 100,000 Pa | ≈ 1 atm |
| Atmosphere | atm | 101,325 Pa | 760 mmHg |
| Pound per sq inch | psi | 6,894.76 Pa | ≈ 0.0689 bar |
| Millimetres of mercury | mmHg / Torr | 133.322 Pa | 1/760 atm |
| Megapascal | MPa | 1,000,000 Pa | 10 bar |
| Application | Typical Pressure | Unit |
|---|---|---|
| Standard atmospheric pressure | 101,325 | Pa (1 atm) |
| Normal blood pressure (systolic) | 120 | mmHg |
| Normal blood pressure (diastolic) | 80 | mmHg |
| Car tyre (typical UK) | 30–35 | psi (2.0–2.4 bar) |
| Bicycle tyre (road) | 80–130 | psi (5.5–9 bar) |
| Scuba tank (full) | 200–300 | bar |
| Deep ocean (10,000 m) | ≈ 100 | MPa (1,000 bar) |
| Hydraulic car jack | 10–20 | MPa |
In a static fluid (liquid or gas), pressure increases with depth. This is why deep-sea vehicles must withstand enormous pressure.
Worked Example: Pressure at 5 m depth in fresh water: P = 1,000 × 9.8 × 5 = 49,000 Pa (49 kPa) above atmospheric pressure. Total absolute pressure = 49,000 + 101,325 = 150,325 Pa.
Key principles:
The atmosphere exerts pressure on all surfaces due to the weight of the air column above. Standard sea level pressure is 101,325 Pa (1 atm). Atmospheric pressure decreases with altitude — at the peak of Ben Nevis (1,345 m), pressure is approximately 86 kPa, causing water to boil at around 95°C rather than 100°C. At the summit of Everest (8,849 m), pressure is only about 33.7 kPa — less than one-third of sea level.
Weather systems use pressure as a key indicator: high-pressure systems (anticyclones) typically bring settled, sunny weather, while low-pressure systems (depressions) bring cloud, rain, and wind.
Blood pressure is measured in millimetres of mercury (mmHg) and expressed as two numbers: systolic (heart contracting) over diastolic (heart relaxing).
Blood pressure categories from NHS guidance. Always consult a healthcare professional for medical advice.
Correct tyre pressure is critical for safety and fuel efficiency. Under-inflated tyres increase rolling resistance (worse fuel economy) and risk overheating at speed. Over-inflated tyres reduce grip and are more susceptible to blowouts. Most UK passenger cars specify pressures of 28–36 psi (1.9–2.5 bar). Always check tyres when cold (driven less than 2 miles).
For a fixed mass of gas at constant temperature, pressure and volume are inversely proportional. Doubling the pressure halves the volume. Applications include:
Pascal's principle states that pressure applied to an enclosed fluid is transmitted equally throughout. This enables hydraulic systems to multiply forces:
A small force on a small piston creates the same pressure throughout the fluid, which acts on a large piston to produce a large output force. Hydraulic systems power car brakes, JCB diggers, aircraft landing gear, and industrial presses.
Example: A 100 N force on a 0.001 m² piston creates 100,000 Pa. Acting on a 0.1 m² piston: Force = 100,000 × 0.1 = 10,000 N (100× multiplication).
Pressure (P) = Force (F) ÷ Area (A). The SI unit is the Pascal (Pa), equal to 1 Newton per square metre (N/m²). Common multiples: kilopascal (kPa = 1,000 Pa), megapascal (MPa = 1,000,000 Pa). Other units include bar, psi (pounds per square inch), atm (atmospheres), and mmHg (millimetres of mercury).
Standard atmospheric pressure at sea level is exactly 101,325 Pa = 101.325 kPa = 1.01325 bar = 14.696 psi = 760 mmHg = 1 atm. This is the average air pressure exerted by the weight of the atmosphere. It decreases with altitude and varies slightly with weather systems.
A healthy adult blood pressure is approximately 120/80 mmHg. The first number (systolic) measures pressure when the heart beats; the second (diastolic) measures pressure between beats. High blood pressure (hypertension) is generally defined as 140/90 mmHg or above. Low blood pressure (hypotension) is typically below 90/60 mmHg. Always consult a GP for advice.
Most UK passenger cars require 28–36 psi (1.9–2.5 bar), but always check the sticker on the driver's door frame or your owner's manual for the correct specification. Front and rear tyres often require different pressures. Some vehicles specify higher pressures when carrying heavy loads or towing. Always check pressures when tyres are cold (not driven more than 1–2 miles).
Boyle's Law states: for a fixed mass of gas at constant temperature, pressure × volume = constant (P₁V₁ = P₂V₂). If volume decreases, pressure increases proportionally. Applications: diving physiology, syringes, bicycle pumps, car engines, weather balloons. At depth, a scuba diver's lungs would occupy less volume — this is why divers must breathe compressed air to compensate.
Fluid pressure increases linearly with depth: P = ρgh, where ρ is density (kg/m³), g = 9.8 N/kg, h = depth (m). For fresh water, pressure increases by about 9,800 Pa per metre of depth (≈ 0.098 bar/m or 1.42 psi/m). At 10 m depth in fresh water, pressure is approximately 98,000 Pa above atmospheric. The sea floor at 11,000 m depth has pressure exceeding 110 MPa (1,100 bar).