There is no doubt that the ancient Egyptians were intrigued by the height of the Entrance from the base of
the Pyramid. For some reason the value 55.6898 was extremely important to them. It is used throughout the
interior. This dimension was very important to the Egyptians, but what does it mean?

The  person that designed the Pyramid had to be extremely intelligent. He  introduced the twelve to one ratio
that allows the design to function and he also knew about the  qualities of  the 1.618033 to 8.618033 ratios
that  take  the  pyramid  to  its  peak. He  made  abundant  use  of ratios  and  multiples  of  the  Entrance  
height. He also  used the base  to  the  Entrance  dimension  throughout  the  Pyramid interior. He made all
the ratios and dimensions work together. Why  this  was  done  we  may  never know, but it was and  it
worked flawlessly

Invoked the 12:1 ratio to create the Pyramid exterior and interior dimensions.           
Split the height, the base and the slant height into sections using 1.618033 to 8.618033.
Used ratios in the interior passageway system.
Used the Entrance to base vertical dimension and the Entrance to base angular dimension throughout the
interior passageway system.

The Great Pyramid of Giza has always been a source of mystery. Experts from all over the world have studied the
greatest structure ever built. Many people have claimed to solve the design of the world’s greatest mystery but no
one has been successful. It has been connected with the earth, the sun, the moon, the stars, space, and even

The mathematics involved in the construction has been deemed by experts to be too advanced for modern man to
understand. This is not true. The mathematics used in the design of the Pyramid is well within the capabilities of any  
mathematician, Egyptian or Modern. This will be shown in this article.

Everyone, no one excepted, forgot about simplicity. Designing ‘simply’ was what the architect did. His methods in
designing the structure were simple but they were wise and ingenious.

Note:  The key to the Pyramid design is the ratio 12:1. This ratio generates the exterior dimensions, the interior
dimensions, and the entrance height of the Pyramid. This is the secret of the Pyramid mathematics.

Using this Design the angles of the Descending and Ascending passageways are 26.565º and 26.565ºrespectively,  at
this stage the bottom of the Great Step is not in the calculations. The Design follows the interior passages to the top
of the Great Step.

The Design angle of the Slant Sides is 51.776º.

Three reference points are used:
1) The Entrance floor height from the base.
2) The Queen’s chamber floor level height from the base.
3) The King’s chamber floor level from the base.

The text and prints in this article will show how every measurement in the Pyramid followed an exact plan and how
the builders managed to obtain accuracy and remain close to this Design, a design similar to the one that they must
have used to accomplish their enormous task.

Every dimension has been calculated to eight places after the point and reduced to four in the prints, for the sake of
accuracy. Angles are accurate to three places after the point. No dimension had digits ‘put in’ to make things work.
The most surprising find in this exercise was the fact that the Entrance floor level height from the base interacts
with every vertical and horizontal interior dimension. This is a very important dimension and its value is 55.6898, it
generates the interior and exterior dimensions accurately.

Inspect a triangle, let’s say 2.5 X 1.25. (Two to one ratio)
The dimension 2.5 is a multiple of the Entrance door height 2.5 X 55.7927 = 139.2245.
The value 1.25 is also a multiple of the Entrance door height 1.25 X 55.7927 = 69.6122.

When you have studied the drawings and you become familiar with the dimensions your perception of the ancient
designers will change forever.

Please use the information supplied, plot it and enjoy, find out that the Great Pyramid dimensions have finally been

Bill McMaster.

Copyright © 2012 [William McMaster]. All Rights Reserved.

An Exercise to show that the Great Pyramid of Giza was designed using Ratios.

The base of the Pyramid in this exercise is 756 (500 cubits  X 18.144”). The half base is 378.

The Rules as applied to the Pyramid Design

1)    The 12:1 ratio generates the height of  the Pyramid, the slant height and the entrance  floor height.

2)    All interior angular and vertical dimensions originate from the Pyramid base.

3)    Ratios apply to all interior horizontal and interior angular dimensions.

4)    All horizontal and vertical dimensions are multiples of the Entrance floor height 55.6898.

Using these rules the Pyramid has a height of 479.94 a slant height of 611.9226 and a half base of 378.
If the base is deemed to be incorrect then a 12:1 ratio has to be constructed for the new base. Every dimension ratio
will remain  in the same proportion.
The first very important find is the ratio 12:1 that positions the Entrance height from the base. (668.2776 : 55.6898).
The distance from the Entrance floor level height to the South face at the same height is 668.2776, exactly twelve
times the door height of 55.6898. Once this ratio was in place all other dimensions can proceed. Since this exercise
only uses the north cross section of the Pyramid this ratio will be 334.1388 : 55.5898 a ratio of six to one. Sir Flinders
Petrie had the height of the entrance correct, he had 668.2”, very close indeed but he missed the 12:1 connection.
Maybe if he had a computer?

One more point on the 12:1 ratio. The Ascending passage passes through the half base (6:1) ratio centre of 334.1388

The base half  length in this exercise is taken as 378and the ratio is 6:1. If you have another dimension that you
would prefer to use then construct a 12:1 ratio for that length. All other dimensions will of course change but will still
be in proportion.

Construct the Design using the prints.

The twelve to one ratio gives the following dimensions:
Pyramid height                  479.94
Pyramid slant height         610.9226   Angle 51º 46' 34"
Pyramid base length         756
Pyramid base half length  378

When the above dimensions have been put in place the most important measurement is 55.6898 the entrance
height from the base, the KEY to all dimensions. It also builds all interior horizontal and vertical ratios.
All interior dimensions are multiples of 55.6898

Queen's Chamber floor height from the pyramid base is 1.25 X 55.6898. (1.25 X the Entrance height from the base)
King's' Chamber floor height from the pyramid base is 2.5 X 55.6898. (2.5 X the Entrance height from the base)
The King's Chamber floor height from the base is twice the Queen's Chamber floor height from the base.
Insert the Descending Passage.                    
Insert the Ascending Passage.
Note the Descending and Ascending angles,26. 565. This is the original design not necessarily what was
accomplished. Time, 4500 years, also has to be factored in. There is a mistake in construction in the ascending
passage that changes the angle to today's measurements. Follow the design measurements and question why the
floor meets the bottom of the Great Step. It becomes quite obvious.
Showing ratios using 55.6898, they are the most important ratios. The dimension 55.6898, (the Entrance height
from the base is shown in red. It is the most important dimension in the Great Pyramid of Giza.
Multiples of 55.6898, the Entrance height from the base The ratios are evident, e.g. 2.5 is 2.5 X 55.6898 = 139.2245.
Three reference points were selected. The Entrance height from the base, The Queen's Chamber floor height from
the base and the King's floor height from the base.

The comparisons between the ancient measurements verified by archaeologists and the design using the 12:1 ratio
are extremely close. The 12:1 design shows how 'it was meant to be'.

It would be almost impossible to construct such an enormous object and keep all the dimensions exactly as it was

                     Today's Measurements        The 12 : 1 Ratio Results               Difference
The Entrance floor                       55.6833                                   55.6898                                   0.0065
The Queen's Chamber floor        69.5650                                   69.6122                                   0.0472
The King's Chamber floor          140.8487                                 139.2245                                   1.6242      
Comparison between the three reference points.
What is the height of the Great Pyramid of Giza
What are the Pyramid of Giza entrance dimensions
What is the slant height of the Great Pyramid of Giza
What is the length of the base of the Great Pyramid of Giza
What are the interior dimensions of the Great Pyramid of Giza
What are the measurements of the Great Pyramid of Giza
What are the dimensions of the Great Pyramid of Giza
What is the height of the Great Pyramid entrance
What is the angle of the Great Pyramid of Giza
How old is the Great Pyramid of Giza
The Great Pyramid of Giza
Showing the 12:1 ratio and the resultant dimensions created. This ratio is the root of all dimensions in the Great
Pyramid of Giza and gives the height, slant height and entrance height values.

Without these values other dimensions cannot be calculated.
The 12:1 ratio is acceptable mathematics for the time the Pyramid was built.
The ancient Egyptians would have used this ratio.
The Great Pyramid of Giza
Entrance Height 55.6898
The difference between the actual measurements and the
measurements in this design. The reference points are extremely
The King's Chamber difference is       1.642
The Queen's Chamber difference is    0.0473
The Entrance difference is                   0.0065
This accuracy proves that this design follows the design used by the Egyptians. The mathematical
descriptions are different of course but the end result is the same. We describe the Entrance
height as 55.6898. How did the Egyptians describe it. Was it cubits or something else, it would be
nice to know. One thing is certain, this measurement was very important to The Pharaoh and his
designers and builders.
RATIOS Built The Great Pyramid
The geometrical layout of the Great Pyramid interior was accomplished by manipulating ratios.
Two lengths were used:

1)    Derived from the Entrance height from the Pyramid Base.                                      55.6898
This ratio was used on horizontal and vertical planes only.

2)    Derived from the Descending passage from the Entrance to the Pyramid Base.   124.5262
This ratio was used on angular planes only.

Both ratios were connected. The start and end of the vertical meets the start and end of the

e.g.   The Ascending passage angular ratio meets the Base to King's Chamber vertical ratio.         

This means that the Passageway angles are controlled by the ratio values and establishes the
original desired Passageway angles at 26.565º and 26.565º respectively,

Their is no reason to today to question what the angles were meant to be.  
Angular ratios derived from the Entrance to the base 124.5262
Vertical and horizontal ratios derived from the Entrance height from the base 55.6898
The end of the ratio section
There is secrecy in the dimensions. The Entrance height is used in almost every dimension. Why? What is 55.6898? Other
than being a part of the 12:1 ratio what does it mean?

Did the ancients use multiples of 1.618 and 8.618?

These dimensions require investigation above all else.

                  And the Pharaoh said "Keep it simple". And It was. And it was done.

                                                  ©Copyright 2012 William McMaster All rights reserved

The ratios shown constitute the only true mathematical
system found in the Great Pyramid.
                         SIMPLE EFFECTIVE MATHEMATICS.
     NO pi NO phi NO aliens.

Please Send Me Your Feedback
Questions, comments, or feedback:
Sir Flinders Petrie (1880) King's Chamber floor height from Base    140.8487
Sir Flinders Petrie (1880) Queen's Chamber floor height from Base  69.5650
Sir Flinders Petrie (1880) Entrance Height from Base                        55.6916
                    Difference between the Sir Flinders Petrie measurements and the Ratio System

(Ratio System) King's Chamber floor height from Base     139.2245     Sir Flinders Petrie  140.8487      Diff. 1.6242
(Ratio System) Queen's Chamber floor height from Base   69.6122     Sir Flinders Petrie    69.5650      Diff.  0.0472
(Ratio System) Entrance Height from Base                         55.6898     Sir Flinders Petrie    55.6916      Diff.  0.0018