Spotlight: Casio fx-451 Calculator

Spotlight: Casio fx-451 Calculator

Quick Facts

Model: fx-451

Company: Casio

Type: Solar Scientific Algebraic

Memory: 1 (store, recall, exchange (X←→M), sum (M+), subtract (M-))

Years in Production: 1985 to 1987 per calculator.org (https://www.calculator.org/calculators/Casio_fx-451.html)

Display: 10 digits

Casio Ledudu’s page on the fx-451: https://casio.ledudu.com/pockets.asp?lg=eng&type=1016

Folding Calculator Power

The Casio fx-451 is a folding scientific calculator. On the left side, there are the arithmetic keys, the shift, mode, and on keys, the display (10 digits), and the solar panel that operates the calculator. The right side has touch, rubber-like, membrane keys. The right side has all the scientific, statistical, fraction, base conversion, and imperial/metric conversions.

You can see my review of the fx-450 from 2018 here: https://edspi31415.blogspot.com/2018/07/retro-review-casio-fx-450-calculator.html

The available modes for the fx-451 are:

. (decimal point): SD (Standard Deviation), single variable statistics. Statistics functions are marked in blue.

0: DEC. Decimal mode. This is also the calculator’s normal/computation mode.

1: BIN. Binary integer mode (base 2). Boolean logic operators are available and are marked in green.

2: OCT. Octal integer mode (base 8). Boolean logic operators are available and are marked in green.

3: HEX. Hexadecimal integer mode (base 16). Boolean logic operators and the letter digits A-F (A=10 to F=15), are available and are marked in green.

4: DEG. Degree angle mode.

5: RAD: Radians angle mode.

6: GRA: Gradians angle mode.

7: FIX: Fixed point decimal setting

8: SCI: Scientific notion decimal setting.

9: NORM: Floating point decimal setting. Numbers less than 0.01 are shown in scientific notation form.

The engineering keys, [ENG] and [←ENG], temporarily show the number in display using scientific notation where the exponents are in multiples of 3 (i.e. 10^-6, 10^-3, 10^0, 10^3, 10^6, etc.)

Like many Casio scientific calculators, the fx-451 sports the fraction key [a b/c], allowing both entry of fractions (proper and mixed), and conversions between fractions and decimal approximations.

In addition, the fx-451 has nine scientific constants. (by pressing [SHIFT] [1-9]).  The constants are:

1. Speed of Light (c)

2. Plank’s constant (h)

3. Universal gravitational constant (G)

4. Electron charge (e)

5. Mass of an electron (me)

6. Atomic mass constant (u)

7. Avogadro’s constant (Na)

8. Boltzmann constant (k)

9. Molar volume of ideal gas (Vm)

All units are in SI units, and are listed with the constant on the keyboard.

The fx-451 Adds Imperial/Metric Conversions

(fx-450 (top), fx-451 (bottom))

The fx-451 is a later version of the fx-450 and has added a set of eight imperial/metric conversions:

Temperature: degrees Fahrenheit/Celsius

Length: inches/millimeters

Volume: gallons/liters, ounces/grams

Mass: pounds/kilograms

Energy: calories/Joules

Pressure: inches of Mercury/kilopascals, atm/megapascals

Conversions are called by the two arrow keys [ ← ] and [ → ], and are they are marked in gold. I always find conversions to be a welcome addition to any calculator.

Solar Power

Like it’s cousin, the fx-450, the fx-451 operates only by solar and light power, hence no other batteries are required.

This is a fun calculator to have, and Casio does a really good job of including lots of features even in its basic scientific calculators.

Eddie

All original content copyright, © 2011-2026. Edward Shore. Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited. This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.

Comparison – Three Generations of Casio fx-115

Casio fx-115D

Casio fx-115MS

Casio fx-115ES Plus

	Casio fx-115D	Casio fx-115MS	Casio fx-115ES Plus
Years (approximate)	1995	2000s	About 2008
Number of Keys	44	50 with keypad	50 with keypad
Number of Digits	10	10	10
Contrast the Screen?	No	Yes	Yes
Modes	[MODE]: Engineering Complex Numbers SD (1-Var Stats) LR (Linear Regression) DEG/RAD/GRAD FIX/SCI/NORM	[MODE]: Comp (Compute) SD (1-Var Stats) REG (2-Var Stats) Deg/Rad/Grad Fix/Sci/Norm Disp (ab/c, d/c, Dot, Comma) Contrast EQN: 2 x 2 linear system, 3 x 3 linear system, quadratic polynomial, cubic polynomial	[MODE]: Comp (Compute) Complex (complex numbers) Stat (Statistics) Base Table (f(x), g(x)) Equation: 2 x 2 linear system , 3 x 3 linear system, quadratic polynomial, cubic polynomial Vector Verify (comparison tests) [SETUP]: MathIO/LinearIO Deg/Rad/Grad Fix/Sci/Norm ab/c vs. d/c STAT (frequencies on) TABLE (f or f an g) Recurring Decimal Display (comma/decimal point) Contrast
Statistics Regressions	Linear	Linear, Logarithmic, Exponential, Power, Inverse, Quadratic	Linear, Quadratic, Logarithmic, Exponential, Power (both a*b^x and a*x^b), Inverse
Display	One line: classic post-fix notation	2-line display, top: entry, bottom: result	Textbook (can be set to 2-line display)
Exact Answers	Fractions (when they are used)	Fractions	Fractions, Square Root, Pi
Statistical Registers	On the keyboard	In two menus: S-SUM, S-VAR	In a menu: STAT
Statistical Data Entry	With the [M+] button	With the [M+] button	In a table
Multi-statement operations	N/A	Yes (with [ : ] )	Yes (with [ : ] )
Rect to Polar Conversions	View only (exchange answers with X ←→ Y)	E = r, F = θ	X = r, Y = θ Answer is displayed
Polar to Rect Conversions	View only (exchange answers with X ←→ Y)	E = x, F = y	X = x, Y = y Answer is displayed
Calculus Functions	None	Integral, Derivative, Solve for X	Integral, Derivative, Solve for X, Sum, Product
Variables	M, Kin/Kout 1-6	A,B,C,D,E,F,X,Y,M	A,B,C,D,E,F,X,Y,M
Extras	Engineering Symbols	Engineering Symbols	GCD, LMC, Int, Intg, RandInt, Factoring Integers (FACTOR)
Power	Solar/Battery Backup: G927	Solar/Battery Backup: LR44	Solar/Battery Backup: LR44

Eddie

All original content copyright, © 2011-2019. Edward Shore. Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited. This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.

HP Prime and Casio Prizm: Solar Irradiance

Solar Irradiance

The program IRRAD will calculate two properties:

(1)  The solar angle of incidence given the angular elevation and azimuth (from south going “counterclockwise”:  east-north-west) of both the sun and panel.

(2)  The irradiance given by the solar panel. 

Formulas

Angle of Incidence Given Azimuth

Degree mode is assumed, the angle of incidence (θ) is found in the following equation:

cos θ = cos(ep)*sin(es) + sin(ep)*cos(es)*cos(as-ap)

Where:

θ = angle of incidence

es = elevation of the sun

ep = elevation of the panel

as = azimuth of the sun, from south headed towards east, then north, then west

ap = azimuth of the panel, from south headed towards east, then north, then west

Angle of Incidence

Azimuth and Elevation of the Sun and Solar Panel

Calculating Flux Density of Solar Radiation on a Surface

Calculating the flux density (energy) of solar radiation on a surface, Lambert’s Cosine Law is used.  Lambert’s Cosine Law states that the relation between the irradiance of the sun and the angle of incidence. The result is the irradiance of the surface.  Irradiance is the rate of energy (power) over a unit area.  In SI units, irradiance is measured in Watts per square meter (W/m^2).

ls = lb * cos θ

Where:

lb = the sun’s power or irradiance.  Often this is treated as a constant, which is approximately 1367 W/m^2 for extraterrestrial solar power, or approximately 1000 W/m^2 when we are dealing with the Earth’s surface (taking scattering of light into account)

ls = the panel’s power or irradiance

Casio Prizm IRRAD

Deg

“SUN: ELEL, AZI(S)”

?->A:?->B

“PANEL: ELEV, AZI(S)”

?->C:?->D

“IRRADIANCE OF THE SUN”

“(W÷M²)”

cos C * sin A + cos A * sin C * cos(B-D)

cos⁻¹ Ans -> θ

I * cos θ -> S

“INCIDENCE ANGLE”

θ ◢

“IRRADIANCE OF SUN”

S

HP Prime IRRAD

EXPORT IRRAD()

BEGIN

LOCAL es,as,ep,ap,θinc;

LOCAL ib,is;

HAngle:=1;

INPUT({es,as},”Sun”,{“Elev.:”,”Azi (S):”});

INPUT({ep,ap},”Panel”,{“Elev.:”,”Azi (S):”});

INPUT(ib,”Sun’s Irradiance”,”I:”,”W/m^2”);

// angle of incidence

θinc:=ACOS(COS(ep)*SIN(es)+SIN(ep)*COS(es)*COS(as-ap));

MSGBOX(“Incidence Angle = “+θinc);

// Lambert’s Cosine Law

Is:=ib*COS(θinc);

MSGBOX(“Surface Irradiance = “+is);

RETURN {θinc,is};

END;

Example

Data:

Sun: 

Elevation:  55⁰24’21” ≈ 55.40583⁰

Azimuth:  175⁰15’44” ≈ 175.26222⁰

Panel:

Elevation:  40⁰

Azimuth:  90⁰ (panel is facing due east)

Irradiance of the Sun:  1000 W/m^2

Output:

Incidence Angle ≈ 48.643169⁰

Surface Radiance ≈ 660.746510 W/m^2

Sources:

Baldocchi, Dennis “Lecture 7, Solar Radiation, Part 3, Earth-Sun Geometry”  Biometeorogy, ESPM 129  University of California, Berkeley.

http://nature.berkeley.edu/biometlab/espm129/notes/Lecture%207%20Solar%20Radiation%20Part%203%20Earth%20Sun%20Geometry%20notes.pdf

Retrieved February 17, 2015. 

Mortimer, David  “Lambert’s Cosine Law”  30 January 2014.  The Solar Bucket.

http://thesolarbucket.blogspot.com/2014/01/lamberts-cosine-law.html

Retrieved March 18, 2015

University of Oregon Solar Radiation Monitoring Laboratory  “Solar Radiation Basics”  University of Oregon.  http://solardat.uoregon.edu/SolarRadiationBasics.html   Retrieved February 10, 2015

This blog is property of Edward Shore – 2015.