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Kramer's Dendrometer

Measurement of tree height and partitioning of volume

General description

The Dendrometer (according to Kramer) is a simple measurement device that is suitable for the estimation of basal area per hectare based on the principle of Bitterlich sampling, stand volume and rough estimates of tree height and volume partitioning of single trees (Kramer 1990[1], Akca 2001[2]). The Dendrometer II is manufactured and distributed by the Department of Forest Inventory and Remote Sensing at the university of Göttingen based on details developed by Prof. Kramer in the early 1980s. Kramer's idea was to develop a simple and affordable alternative to the Mirror Relascope developed based on Walter Bitterlich's invention of the "angle count method".

Height measurement

It is possible to roughly estimate tree height based on the geometric principle with the Dendrometer. Therefore hold the device vertically in front of the eye (opening on top) and aim at the tree to be measured. Adjust the distance of the Dendrometer from the eye or your distance from the tree until the points k and h correspond to the tree tip resp. to the bottom of the trunk. The relation of the section hi to line hk is 1:10. the height of point i corresponds to 1/10 of the tree height. In order to calculate the tree’s height measure the distance from i on the tree to the tree base and multiply by 10. It should be considered that the measurement of tree heights is just a "side function" of this device, while the main purpose is in estimation basal area.

Estimation of basal area per hectare

The estimation of basal area is based on the principle of relascope sampling invented by Walter Bitterlich (Bitterlich 1952[3]). Aim at the dbh of each tree in a 360° sweep (from your standpoint). The basal area is a function of the angle and the number of stems which appear wider than the respective angle opening. Trees with width smaller than fg are not included in the sample (counted). If you hold the dendrometer vertically at a distance of 50 cm before the eye r (distance to the eye is fixed with rs is 50 cm), then the plate with the width 1 creates an angle for which every counted tree corresponds to 1 m² basal area per hectare (basal area factor = 1).

When a width of 2 or 4 is used, the resulting basal area (number of trees counted) must be multiplied by the corresponding factor (2 or 4) in order to obtain estimates of basal area per hectare. With relascope sampling on slopes it is necessary to multiply the estimated basal area per hectare with the coefficient k (k=1/cos α) for the respective maximal inclination of slope from the table on the Dendrometer.

Determining value of single trees by estimating volume sections

Set up the dendrometer in the same way as for height measurement. Through the markings b, c, d the stem is divided to 4 sections of equal volume.

Estimating stem volume with "form height"

For the 4 main tree species in northern Germany (Ei, Bu, Fi, Ki) and a given or measured mean stand height (hm, which should be approximately the height of the mean basal area tree) the "form-height factor" (FH-Tarif) can be read off the table on the dendrometer. Calculate stand volume per hectare in m³ including bark with the formula \(V=G*FH \,\).

Instruction manual

Thanks to the input and efforts of many international researchers visiting our department, a lot of translations are available for the short instruction manual. It can be downloaded in:


  1. Kramer, H. 1990. Nutzungsplanung in der Forsteinrichtung. 2., überarbeitete und erweiterte Auflage. J.D. Sauerländer’s Verlag, Frankfurt/Main.
  2. Akca, A. 2001. Waldinventur. J.D. Sauerländer's Verlag. Frankfurt am Main, 193 S.
  3. BITTERLICH, W., 1952. Die Winkelzählprobe. Forstwissenschaftliches Centralblatt, 215-225.
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