What is the formula for pressure?

Pressure is force per unit area: P = F / A. In SI units: Pa = N / m².

What is the difference between gauge and absolute pressure?

Gauge pressure is measured relative to ambient atmospheric pressure. Absolute pressure adds atmospheric pressure: P_abs = P_gauge + P_atm.

Which units can I use?

Pressure: Pa, kPa, MPa, bar, atm, psi, torr. Force: N, kN, lbf, kgf. Area: m², cm², mm², in², ft².

How do I calculate hydrostatic pressure?

Use P = ρ g h for gauge pressure. For absolute pressure, add atmospheric pressure: P_abs = ρ g h + P_atm.

Can pressure be negative?

Gauge pressure can be negative when the measured pressure is below atmospheric (vacuum). Absolute pressure is always non‑negative.

What density and gravity should I use for fluids?

Use the fluid’s actual density at temperature (e.g., water ≈ 1000 kg/m³ near 4 °C). Use local g if needed; standard gravity is 9.80665 m/s².

Pressure Calculator

Professional pressure calculator for physics and engineering. Compute pressure from force and area, force from pressure and area, or hydrostatic pressure. Includes unit conversions (Pa, kPa, bar, atm, psi) and WCAG 2.1 AA accessibility.

Pressure Calculator

This professional-grade pressure calculator helps students, engineers, and scientists compute: pressure from force and area, force from pressure and area, or hydrostatic pressure. It includes precise unit conversions, clear explanations, and WCAG 2.1 AA accessible design.

Pressure (F ÷ A)

Force (P × A)

Area (F ÷ P)

Hydrostatic (ρ g h)

Force *

Area *

Output pressure unit

Pressure *

Area *

Output force unit

Force *

Pressure *

Output area unit

Fluid density ρ *

Depth h *

Gravity g

Standard g (9.80665 m/s²)

Custom g

Pressure type

Gauge (ρgh)

Absolute (ρgh + Patm)

Output pressure unit

Results

Your results will appear here. Unit conversions are included for convenience.

Data Source and Methodology

BIPM, The International System of Units (SI Brochure), 9th Edition (2019). Retrieved from https://www.bipm.org/en/publications/si-brochure
NIST, CODATA Recommended Values of the Fundamental Physical Constants (2022). Retrieved from https://physics.nist.gov/cuu/Constants/
IAPWS, Release on the IAPWS Formulation 1995 for the Thermodynamic Properties of Ordinary Water Substance (IAPWS‑95). Retrieved from https://www.iapws.org

Tutti i calcoli si basano rigorosamente sulle formule e sui dati forniti da questa fonte.

The Formula Explained

Core definition:

$$ P = \\frac{F}{A} $$

Rearrangements:

$$ F = P \\cdot A \\quad\\text{and}\\quad A = \\frac{F}{P} $$

Hydrostatic (gauge) pressure:

$$ P_{\\text{gauge}} = \\rho \\; g \\; h $$

Absolute pressure:

$$ P_{\\text{abs}} = P_{\\text{gauge}} + P_{\\text{atm}} $$

SI units: Pa = N/m², 1 bar = 10^5 Pa, 1 atm = 101\,325 Pa, 1 psi ≈ 6\,894.757 Pa.

Glossary of Variables

P (Pressure): The force applied per unit area. Units: Pa, kPa, MPa, bar, atm, psi, torr.
F (Force): A push or pull on an object. Units: N, kN, lbf, kgf.
A (Area): Surface over which the force acts. Units: m², cm², mm², in², ft².
ρ (Density): Mass per unit volume of a fluid. Units: kg/m³, g/cm³.
g (Gravity): Acceleration due to gravity. Default standard g = 9.80665 m/s².
h (Depth): Vertical distance below the free surface. Units: m, ft.
P_atm (Atmospheric pressure): Ambient pressure. Defaults to 101.325 kPa at sea level.

How It Works: A Step-by-Step Example

Suppose a 500 N force is uniformly applied over an area of 0.02 m². What is the pressure?

Identify inputs: F = 500 N, A = 0.02 m².
Apply the definition P = F / A.
Compute: P = 500 ÷ 0.02 = 25,000 Pa.
Convert units: 25,000 Pa = 25 kPa ≈ 0.246 bar ≈ 3.63 psi ≈ 0.247 atm × 10 (i.e., 0.247 atm is incorrect here; correct is 25,000 / 101,325 ≈ 0.247 atm).

The calculator performs these steps instantly and lists results across common units.

Frequently Asked Questions (FAQ)

Is pressure always uniform across a surface?

No. Pressure can vary across a surface. The formula P = F/A assumes uniform distribution or uses average values.

What’s the difference between Pa, kPa, MPa, and bar?

They are metric pressure units. 1 kPa = 1,000 Pa; 1 MPa = 1,000,000 Pa; 1 bar = 100,000 Pa.

How do I convert between psi and kPa?

1 psi = 6.894757 kPa. Multiply psi by 6.894757 to get kPa; divide kPa by 6.894757 to get psi.

Should I use gauge or absolute pressure?

Use gauge when comparing to ambient conditions (e.g., tires). Use absolute for thermodynamics or when zero reference must be vacuum.

Does temperature affect hydrostatic pressure?

Indirectly, through density. Warmer fluids are typically less dense, slightly reducing ρgh.

Can I use this calculator for gases?

Yes, the P = F/A relationship is general. For hydrostatics in gases, ρ is small; ρgh may be negligible over modest heights.

What accuracy does the tool use?

Exact arithmetic based on SI definitions and high-precision conversion factors. Display is rounded for readability.

Audit: Complete

Formula (LaTeX) + variables + units

This section shows the formulas used by the calculator engine, plus variable definitions and units.

Formula (extracted LaTeX)

\[','\]

','

Formula (extracted LaTeX)

\[P = \\frac{F}{A}\]

P = \\frac{F}{A}

Formula (extracted LaTeX)

\[F = P \\cdot A \\quad\\text{and}\\quad A = \\frac{F}{P}\]

F = P \\cdot A \\quad\\text{and}\\quad A = \\frac{F}{P}

Formula (extracted LaTeX)

\[P_{\\text{gauge}} = \\rho \\; g \\; h\]

P_{\\text{gauge}} = \\rho \\; g \\; h

Formula (extracted LaTeX)

\[P_{\\text{abs}} = P_{\\text{gauge}} + P_{\\text{atm}}\]

P_{\\text{abs}} = P_{\\text{gauge}} + P_{\\text{atm}}

Formula (extracted text)

Core definition: $ P = \\frac{F}{A} $ Rearrangements: $ F = P \\cdot A \\quad\\text{and}\\quad A = \\frac{F}{P} $ Hydrostatic (gauge) pressure: $ P_{\\text{gauge}} = \\rho \\; g \\; h $ Absolute pressure: $ P_{\\text{abs}} = P_{\\text{gauge}} + P_{\\text{atm}} $ SI units: Pa = N/m², 1 bar = 10^5 Pa, 1 atm = 101\,325 Pa, 1 psi ≈ 6\,894.757 Pa.

Variables and units

No variables provided in audit spec.

Sources (authoritative):

NIST — Weights and measures — nist.gov · Accessed 2026-01-19
https://www.nist.gov/pml/weights-and-measures
FTC — Consumer advice — consumer.ftc.gov · Accessed 2026-01-19
https://consumer.ftc.gov/

Changelog

Version: 0.1.0-draft
Last code update: 2026-01-19

0.1.0-draft · 2026-01-19

Initial audit spec draft generated from HTML extraction (review required).
Verify formulas match the calculator engine and convert any text-only formulas to LaTeX.
Confirm sources are authoritative and relevant to the calculator methodology.

Verified by Ugo Candido on 2026-01-19
Profile · LinkedIn

Full original guide (expanded)

Pressure Calculator

Pressure (F ÷ A)

Force (P × A)

Area (F ÷ P)

Hydrostatic (ρ g h)

Force *

Area *

Output pressure unit

Pressure *

Area *

Output force unit

Force *

Pressure *

Output area unit

Fluid density ρ *

Depth h *

Gravity g

Standard g (9.80665 m/s²)

Custom g

Pressure type

Gauge (ρgh)

Absolute (ρgh + Patm)

Output pressure unit

Results

Your results will appear here. Unit conversions are included for convenience.

Data Source and Methodology

BIPM, The International System of Units (SI Brochure), 9th Edition (2019). Retrieved from https://www.bipm.org/en/publications/si-brochure
NIST, CODATA Recommended Values of the Fundamental Physical Constants (2022). Retrieved from https://physics.nist.gov/cuu/Constants/
IAPWS, Release on the IAPWS Formulation 1995 for the Thermodynamic Properties of Ordinary Water Substance (IAPWS‑95). Retrieved from https://www.iapws.org

Tutti i calcoli si basano rigorosamente sulle formule e sui dati forniti da questa fonte.

The Formula Explained

Core definition:

$$ P = \\frac{F}{A} $$

Rearrangements:

$$ F = P \\cdot A \\quad\\text{and}\\quad A = \\frac{F}{P} $$

Hydrostatic (gauge) pressure:

$$ P_{\\text{gauge}} = \\rho \\; g \\; h $$

Absolute pressure:

$$ P_{\\text{abs}} = P_{\\text{gauge}} + P_{\\text{atm}} $$

SI units: Pa = N/m², 1 bar = 10^5 Pa, 1 atm = 101\,325 Pa, 1 psi ≈ 6\,894.757 Pa.

Glossary of Variables

P (Pressure): The force applied per unit area. Units: Pa, kPa, MPa, bar, atm, psi, torr.
F (Force): A push or pull on an object. Units: N, kN, lbf, kgf.
A (Area): Surface over which the force acts. Units: m², cm², mm², in², ft².
ρ (Density): Mass per unit volume of a fluid. Units: kg/m³, g/cm³.
g (Gravity): Acceleration due to gravity. Default standard g = 9.80665 m/s².
h (Depth): Vertical distance below the free surface. Units: m, ft.
P_atm (Atmospheric pressure): Ambient pressure. Defaults to 101.325 kPa at sea level.

How It Works: A Step-by-Step Example

Suppose a 500 N force is uniformly applied over an area of 0.02 m². What is the pressure?

Identify inputs: F = 500 N, A = 0.02 m².
Apply the definition P = F / A.
Compute: P = 500 ÷ 0.02 = 25,000 Pa.
Convert units: 25,000 Pa = 25 kPa ≈ 0.246 bar ≈ 3.63 psi ≈ 0.247 atm × 10 (i.e., 0.247 atm is incorrect here; correct is 25,000 / 101,325 ≈ 0.247 atm).

The calculator performs these steps instantly and lists results across common units.

Frequently Asked Questions (FAQ)

Is pressure always uniform across a surface?

No. Pressure can vary across a surface. The formula P = F/A assumes uniform distribution or uses average values.

What’s the difference between Pa, kPa, MPa, and bar?

They are metric pressure units. 1 kPa = 1,000 Pa; 1 MPa = 1,000,000 Pa; 1 bar = 100,000 Pa.

How do I convert between psi and kPa?

1 psi = 6.894757 kPa. Multiply psi by 6.894757 to get kPa; divide kPa by 6.894757 to get psi.

Should I use gauge or absolute pressure?

Use gauge when comparing to ambient conditions (e.g., tires). Use absolute for thermodynamics or when zero reference must be vacuum.

Does temperature affect hydrostatic pressure?

Indirectly, through density. Warmer fluids are typically less dense, slightly reducing ρgh.

Can I use this calculator for gases?

Yes, the P = F/A relationship is general. For hydrostatics in gases, ρ is small; ρgh may be negligible over modest heights.

What accuracy does the tool use?

Exact arithmetic based on SI definitions and high-precision conversion factors. Display is rounded for readability.

Audit: Complete

Formula (LaTeX) + variables + units

This section shows the formulas used by the calculator engine, plus variable definitions and units.

Formula (extracted LaTeX)

\[','\]

','

Formula (extracted LaTeX)

\[P = \\frac{F}{A}\]

P = \\frac{F}{A}

Formula (extracted LaTeX)

\[F = P \\cdot A \\quad\\text{and}\\quad A = \\frac{F}{P}\]

F = P \\cdot A \\quad\\text{and}\\quad A = \\frac{F}{P}

Formula (extracted LaTeX)

\[P_{\\text{gauge}} = \\rho \\; g \\; h\]

P_{\\text{gauge}} = \\rho \\; g \\; h

Formula (extracted LaTeX)

\[P_{\\text{abs}} = P_{\\text{gauge}} + P_{\\text{atm}}\]

P_{\\text{abs}} = P_{\\text{gauge}} + P_{\\text{atm}}

Formula (extracted text)

Core definition: $ P = \\frac{F}{A} $ Rearrangements: $ F = P \\cdot A \\quad\\text{and}\\quad A = \\frac{F}{P} $ Hydrostatic (gauge) pressure: $ P_{\\text{gauge}} = \\rho \\; g \\; h $ Absolute pressure: $ P_{\\text{abs}} = P_{\\text{gauge}} + P_{\\text{atm}} $ SI units: Pa = N/m², 1 bar = 10^5 Pa, 1 atm = 101\,325 Pa, 1 psi ≈ 6\,894.757 Pa.

Variables and units

No variables provided in audit spec.

Sources (authoritative):

NIST — Weights and measures — nist.gov · Accessed 2026-01-19
https://www.nist.gov/pml/weights-and-measures
FTC — Consumer advice — consumer.ftc.gov · Accessed 2026-01-19
https://consumer.ftc.gov/

Changelog

Version: 0.1.0-draft
Last code update: 2026-01-19

0.1.0-draft · 2026-01-19

Initial audit spec draft generated from HTML extraction (review required).
Verify formulas match the calculator engine and convert any text-only formulas to LaTeX.
Confirm sources are authoritative and relevant to the calculator methodology.

Verified by Ugo Candido on 2026-01-19
Profile · LinkedIn

Pressure Calculator

Pressure (F ÷ A)

Force (P × A)

Area (F ÷ P)

Hydrostatic (ρ g h)

Force *

Area *

Output pressure unit

Pressure *

Area *

Output force unit

Force *

Pressure *

Output area unit

Fluid density ρ *

Depth h *

Gravity g

Standard g (9.80665 m/s²)

Custom g

Pressure type

Gauge (ρgh)

Absolute (ρgh + Patm)

Output pressure unit

Results

Your results will appear here. Unit conversions are included for convenience.

Data Source and Methodology

BIPM, The International System of Units (SI Brochure), 9th Edition (2019). Retrieved from https://www.bipm.org/en/publications/si-brochure
NIST, CODATA Recommended Values of the Fundamental Physical Constants (2022). Retrieved from https://physics.nist.gov/cuu/Constants/
IAPWS, Release on the IAPWS Formulation 1995 for the Thermodynamic Properties of Ordinary Water Substance (IAPWS‑95). Retrieved from https://www.iapws.org

Tutti i calcoli si basano rigorosamente sulle formule e sui dati forniti da questa fonte.

The Formula Explained

Core definition:

$$ P = \\frac{F}{A} $$

Rearrangements:

$$ F = P \\cdot A \\quad\\text{and}\\quad A = \\frac{F}{P} $$

Hydrostatic (gauge) pressure:

$$ P_{\\text{gauge}} = \\rho \\; g \\; h $$

Absolute pressure:

$$ P_{\\text{abs}} = P_{\\text{gauge}} + P_{\\text{atm}} $$

SI units: Pa = N/m², 1 bar = 10^5 Pa, 1 atm = 101\,325 Pa, 1 psi ≈ 6\,894.757 Pa.

Glossary of Variables

P (Pressure): The force applied per unit area. Units: Pa, kPa, MPa, bar, atm, psi, torr.
F (Force): A push or pull on an object. Units: N, kN, lbf, kgf.
A (Area): Surface over which the force acts. Units: m², cm², mm², in², ft².
ρ (Density): Mass per unit volume of a fluid. Units: kg/m³, g/cm³.
g (Gravity): Acceleration due to gravity. Default standard g = 9.80665 m/s².
h (Depth): Vertical distance below the free surface. Units: m, ft.
P_atm (Atmospheric pressure): Ambient pressure. Defaults to 101.325 kPa at sea level.

How It Works: A Step-by-Step Example

Suppose a 500 N force is uniformly applied over an area of 0.02 m². What is the pressure?

Identify inputs: F = 500 N, A = 0.02 m².
Apply the definition P = F / A.
Compute: P = 500 ÷ 0.02 = 25,000 Pa.
Convert units: 25,000 Pa = 25 kPa ≈ 0.246 bar ≈ 3.63 psi ≈ 0.247 atm × 10 (i.e., 0.247 atm is incorrect here; correct is 25,000 / 101,325 ≈ 0.247 atm).

The calculator performs these steps instantly and lists results across common units.

Frequently Asked Questions (FAQ)

Is pressure always uniform across a surface?

No. Pressure can vary across a surface. The formula P = F/A assumes uniform distribution or uses average values.

What’s the difference between Pa, kPa, MPa, and bar?

They are metric pressure units. 1 kPa = 1,000 Pa; 1 MPa = 1,000,000 Pa; 1 bar = 100,000 Pa.

How do I convert between psi and kPa?

1 psi = 6.894757 kPa. Multiply psi by 6.894757 to get kPa; divide kPa by 6.894757 to get psi.

Should I use gauge or absolute pressure?

Use gauge when comparing to ambient conditions (e.g., tires). Use absolute for thermodynamics or when zero reference must be vacuum.

Does temperature affect hydrostatic pressure?

Indirectly, through density. Warmer fluids are typically less dense, slightly reducing ρgh.

Can I use this calculator for gases?

Yes, the P = F/A relationship is general. For hydrostatics in gases, ρ is small; ρgh may be negligible over modest heights.

What accuracy does the tool use?

Exact arithmetic based on SI definitions and high-precision conversion factors. Display is rounded for readability.

Audit: Complete

Formula (LaTeX) + variables + units

This section shows the formulas used by the calculator engine, plus variable definitions and units.

Formula (extracted LaTeX)

\[','\]

','

Formula (extracted LaTeX)

\[P = \\frac{F}{A}\]

P = \\frac{F}{A}

Formula (extracted LaTeX)

\[F = P \\cdot A \\quad\\text{and}\\quad A = \\frac{F}{P}\]

F = P \\cdot A \\quad\\text{and}\\quad A = \\frac{F}{P}

Formula (extracted LaTeX)

\[P_{\\text{gauge}} = \\rho \\; g \\; h\]

P_{\\text{gauge}} = \\rho \\; g \\; h

Formula (extracted LaTeX)

\[P_{\\text{abs}} = P_{\\text{gauge}} + P_{\\text{atm}}\]

P_{\\text{abs}} = P_{\\text{gauge}} + P_{\\text{atm}}

Formula (extracted text)

Core definition: $ P = \\frac{F}{A} $ Rearrangements: $ F = P \\cdot A \\quad\\text{and}\\quad A = \\frac{F}{P} $ Hydrostatic (gauge) pressure: $ P_{\\text{gauge}} = \\rho \\; g \\; h $ Absolute pressure: $ P_{\\text{abs}} = P_{\\text{gauge}} + P_{\\text{atm}} $ SI units: Pa = N/m², 1 bar = 10^5 Pa, 1 atm = 101\,325 Pa, 1 psi ≈ 6\,894.757 Pa.

Variables and units

No variables provided in audit spec.

Sources (authoritative):

NIST — Weights and measures — nist.gov · Accessed 2026-01-19
https://www.nist.gov/pml/weights-and-measures
FTC — Consumer advice — consumer.ftc.gov · Accessed 2026-01-19
https://consumer.ftc.gov/

Changelog

Version: 0.1.0-draft
Last code update: 2026-01-19

0.1.0-draft · 2026-01-19

Initial audit spec draft generated from HTML extraction (review required).
Verify formulas match the calculator engine and convert any text-only formulas to LaTeX.
Confirm sources are authoritative and relevant to the calculator methodology.

Verified by Ugo Candido on 2026-01-19
Profile · LinkedIn

Formulas

(Formulas preserved from original page content, if present.)

Version 0.1.0-draft

Citations

Add authoritative sources relevant to this calculator (standards bodies, manuals, official docs).

Changelog

0.1.0-draft — 2026-01-19: Initial draft (review required).

Pressure Calculator

Pressure Calculator

Interactive Calculator

Results

Data Source and Methodology

The Formula Explained

Glossary of Variables

How It Works: A Step-by-Step Example

Frequently Asked Questions (FAQ)

Is pressure always uniform across a surface?

What’s the difference between Pa, kPa, MPa, and bar?

How do I convert between psi and kPa?

Should I use gauge or absolute pressure?

Does temperature affect hydrostatic pressure?

Can I use this calculator for gases?

What accuracy does the tool use?

Full original guide (expanded)

Pressure Calculator

Interactive Calculator

Results

Data Source and Methodology

The Formula Explained

Glossary of Variables

How It Works: A Step-by-Step Example

Frequently Asked Questions (FAQ)

Is pressure always uniform across a surface?

What’s the difference between Pa, kPa, MPa, and bar?

How do I convert between psi and kPa?

Should I use gauge or absolute pressure?

Does temperature affect hydrostatic pressure?

Can I use this calculator for gases?

What accuracy does the tool use?

Pressure Calculator

Interactive Calculator

Results

Data Source and Methodology

The Formula Explained

Glossary of Variables

How It Works: A Step-by-Step Example

Frequently Asked Questions (FAQ)

Is pressure always uniform across a surface?

What’s the difference between Pa, kPa, MPa, and bar?

How do I convert between psi and kPa?

Should I use gauge or absolute pressure?

Does temperature affect hydrostatic pressure?

Can I use this calculator for gases?

What accuracy does the tool use?