Beedy Academy · Calculators

Unit conversions and everyday plant math

Unit conversions, tank volumes and everyday math. Each calculator shows its formula and offers practice problems.

Unit conversions

Pressure converter

Formulay = x × f₁ ÷ f₂ · 1 bar = 100 000 Pa · 1 psi = 6 894.757 Pa · 1 atm = 101 325 Pa

Value to convert (x)

From unit

Pressure—bar

Pressure—Pa

Pressure—kPa

Pressure—mbar

Pressure—psi

Pressure—atm

Pressure—m H₂O

Pressure—mmHg

Pressure—in H₂O

Pressure—kgf/cm²

For psi, bar and kPa, say whether it is gauge (g) or absolute (a): absolute = gauge + atmospheric pressure (≈ 101.3 kPa at sea level). The torr (1/760 atm) is practically equal to the mmHg.

Flow rate converter

Formulay = x × f₁ ÷ f₂ · 1 gal US = 3.785 411 784 L · 1 gal imp. = 4.546 09 L · 1 bbl = 42 gal US

Value to convert (x)

From unit

Flow rate—m³/h

Flow rate—m³/d

Flow rate—L/s

Flow rate—L/min

Flow rate—US gpm

Flow rate—imp gpm

Flow rate—bbl/d

Flow rate—MGD (US)

US gallon = 3.785 L; imperial gallon = 4.546 L: check which one the flowmeter shows. 1 barrel (bbl) = 42 US gallons = 158.99 L.

Temperature converter

Formula°F = °C × 1.8 + 32 · K = °C + 273.15

Value to convert (x)

From unit

Temperature—°C

Temperature—°F

Temperature—K

A temperature difference of 1 °C equals 1 K and 1.8 °F: when converting a difference, do not add 32.

Length converter

Formulay = x × f₁ ÷ f₂ · 1 in = 25.4 mm · 1 ft = 0.3048 m · 1 mi = 1 609.344 m

Value to convert (x)

From unit

Length—ft

Length—m

Length—mm

Length—cm

Length—km

Length—in

Length—yd

Length—mi

The inch is exactly 25.4 mm and the foot 0.3048 m (1959 international definition).

Volume converter

Formulay = x × f₁ ÷ f₂ · 1 ft³ = 28.316 846 592 L · 1 bbl = 158.987 294 928 L

Value to convert (x)

From unit

Volume—US gal

Volume—m³

Volume—L

Volume—imp gal

Volume—ft³

Volume—bbl

For a tank, check whether the gauge reads in US or imperial gallons: they differ by about 20 %.

Mass converter

Formulay = x × f₁ ÷ f₂ · 1 lb = 0.453 592 37 kg · 1 t = 1000 kg

Value to convert (x)

From unit

Mass—lb

Mass—kg

Mass—g

Mass—t

Mass—short ton

Mass—long ton

The metric tonne (1000 kg) differs from the short ton (2000 lb = 907.2 kg) and the long ton (2240 lb = 1016 kg).

Energy converter

Formulay = x × f₁ ÷ f₂ · 1 kWh = 3.6 MJ · 1 BTU = 1.055 055 852 62 kJ · 1 kcal = 4.1868 kJ

Value to convert (x)

From unit

Energy—kWh

Energy—MJ

Energy—kJ

Energy—BTU

Energy—kcal

BTU and kcal are International Table (IT) values. Natural gas is often metered in GJ or therms (1 therm = 100 000 BTU).

Power converter

Formulay = x × f₁ ÷ f₂ · 1 hp = 745.700 W · 1 TR = 12 000 BTU/h = 3.517 kW

Value to convert (x)

From unit

Power—kW

Power—W

Power—hp

Power—hp (metric)

Power—BTU/h

Power—TR

hp = mechanical horsepower (550 ft·lbf/s = 745.7 W); metric hp = 735.5 W. 1 ton of refrigeration (TR) = 12 000 BTU/h.

Geometry and tank volumes

Rectangular basin (box)

FormulaA = a × b · V = a × b × h · S = 2 (ab + ah + bh)

Length (a)m

Width (b)m

Height (h)m

Base area (A)—m²

Volume (V)—m³

Volume in litres—L

Total surface (S)—m²

Use the inside dimensions for the working volume. 1 m³ = 1000 L.

Cylindrical tank

FormulaA = π D² ÷ 4 · V = A × h

Inside diameter (D)m

Height (h)m

Base area (A)—m²

Volume (V)—m³

Volume in litres—L

For a vertical tank, h can be the liquid level: the result is then the volume held.

Cone and hopper (frustum)

FormulaV = π h (D₁² + D₁D₂ + D₂²) ÷ 12 · θ = atan(2h ÷ (D₁ − D₂))

Large diameter, top (D₁)m

Small diameter, bottom (D₂)m

Height (h)m

Volume (V)—m³

Volume in litres—L

Wall angle from horizontal (θ)—°

D₂ = 0 gives a full cone. For a solids hopper, a steeper wall (often 60° or more) helps the material flow.

Sphere

FormulaV = π D³ ÷ 6 · S = π D²

Inside diameter (D)m

Volume (V)—m³

Volume in litres—L

Surface area (S)—m²

The surface area is used to estimate paint or insulation; the volume gives the capacity of a storage sphere.

Level → volume (rectangular tank)

FormulaV = a × b × h · % = h ÷ H × 100 · V_libre = a × b × (H − h)

Length (a)m

Width (b)m

Total usable height (H)m

Measured level (h)m

Volume held (V)—m³

Fill level—%

Free volume—m³

Volume per centimetre of level—L/cm

The volume per centimetre turns a level drop into the volume pumped or used (pump draw-down test, chemical use).

Everyday math

Rule of three (proportion)

Formuladirect: x = B × C ÷ A · inverse: x = A × B ÷ C

If A…

…gives B

then C gives x

Proportion

Result (x)—

Direct: 2 h of pumping give 50 m³, how much in 3.5 h? Inverse: 2 pumps empty the tank in 6 h, how long with 3 pumps?

Percent change and percent difference

FormulaΔ = B − A · Δ% = (B − A) ÷ A × 100 · δ% = |B − A| ÷ ((A + B) ÷ 2) × 100

Starting value (A)

New value (B)

Difference (Δ)—

Percent change (Δ%)—%

Percent difference (δ%)—%

The percent change is relative to the starting value A. The percent difference is relative to the average of both: use it to compare two instruments or two duplicates.

Weighted average (blending)

Formulax̄_w = (w₁x₁ + w₂x₂ + w₃x₃ + w₄x₄) ÷ (w₁ + w₂ + w₃ + w₄)

Value 1 (x₁)

Weight 1 (w₁)

Value 2 (x₂)

Weight 2 (w₂)

Value 3 (x₃)

Weight 3 (w₃)

Value 4 (x₄)

Weight 4 (w₄)

Weighted average—

Sum of weights—

Blending streams: x = concentration, w = flow or volume of each stream. Set the weight to 0 for an unused line.

Linear interpolation

Formulay = y₁ + (x − x₁) × (y₂ − y₁) ÷ (x₂ − x₁) · t = (x − x₁) ÷ (x₂ − x₁) × 100

Table row 1: x₁

Table row 1: y₁

Table row 2: x₂

Table row 2: y₂

Look-up value (x)

Interpolated value (y)—

Position between the two rows (t)—%

To read a table (water density, steam table, tank strapping chart) between two rows. If t falls outside 0 to 100 %, it is an extrapolation: be careful.

Mean and standard deviation

Formulax̄ = Σxᵢ ÷ n · s = √(Σ(xᵢ − x̄)² ÷ (n − 1)) · CV = s ÷ x̄ × 100

Number of values used (n, 2 to 6)

Value 1 (x₁)

Value 2 (x₂)

Value 3 (x₃)

Value 4 (x₄)

Value 5 (x₅)

Value 6 (x₆)

Mean (x̄)—

Sample standard deviation (s)—

Coefficient of variation (CV)—%

Range (max − min)—

Sample standard deviation (divided by n − 1). Only the first n values count; the others are ignored. The CV is used to judge the repeatability of lab duplicates.

Right triangle and slope (% ↔ degrees)

Formulac = √(a² + b²) · p = a ÷ b × 100 · θ = atan(p ÷ 100) · p = tan(θ) × 100

Rise (a)m

Horizontal run (b)m

Slope to convert to degrees (p)%

Angle to convert to % (θ)°

Sloped length (c)—m

Slope a ÷ b—%

Angle of a ÷ b—°

Slope p in degrees—°

Angle θ as slope—%

A 100 % slope is 45°. Slope uses the horizontal run, not the sloped length. Gravity pipe: 1 % = 1 cm per metre.

Rounding to significant figures

Formulax ≈ m × 10^e · 1 ≤ |m| < 10

Value (x)

Significant figures (n)

Rounded value—

Mantissa (m)—

Exponent (e)—

An exact 5 is rounded up (some lab standards round it to the even digit). Keep every digit during the calculation and round only the final result.

Learning and checking tools. The ranges shown are general guidance: always follow your plant's procedures, permits and set points. Nothing is sent anywhere: the calculations run in your browser.

Unit conversions and everyday plant math